Premium indexing in lifelong health insurance
|
|
- Meghan Webster
- 8 years ago
- Views:
Transcription
1 Premium indexing in lifelong healh insurance W. Vercruysse 1, J. Dhaene 1, M. Denui 2, E. Piacco 3, K. Anonio 4 1 KU Leuven, Belgium 2 U.C.L., Louvain-la-Neuve, Belgium 3 Universià di Triese, Triese, Ialy 4 Universiy of Amserdam, The Neherlands, and KU Leuven, Belgium Absrac For lifelong healh insurance covers, medical in aion no incorporaed in he level premiums deermined a policy issue requires an appropriae increase of hese premiums and/or he corresponding reserves during he erm of he conrac. In his paper, we invesigae appropriae premium indexing mechanisms, based on a given medical in aion index. Firs, we consider a general relaion beween bene, premium and reserve increases, which can be used on a yearly basis o resore he acuarial equivalence ha is broken due o observed medical in aion over he pas year. Nex, we consider an individual premium indexing mechanism, depending on he age a policy issue, which makes he relaive premium increases above he observed medical in aion more sable over ime. Finally, we consider an aggregae premium indexing mechanism for a porfolio of new enrans, where he relaive premium increase above observed in aion is independen of age-a-enry, inroducing inergeneraional solidariy. Key words: medical expense insurance, lifelong conrac, medical in- aion index, reserve. This work is performed as par of he AG Insurance Chair on Healh Insurance a KU Leuven. 1
2 1 Inroducion We consider healh insurance conracs, more speci cally medical expense reimbursemen policies (or forfeiure daily allowance policies) o ered as erm or lifelong insurance covers wih level premiums. As is he case in life insurance, level premiums lead o asse accumulaion in a reserve. In general, he bene s ha will be paid over he years for a erm or lifelong healh insurance porfolio will be impaced by a number of unpredicable facors, such as changes in prices for medical goods and services and demographic evoluions of he insured populaion. Given he long-erm naure of healh insurance conracs and he impossibiliy o predic or hedge agains medical in aion, insurers ofen do no ake ino accoun or are no able o fully accoun for his medical in aion in he seing of he premium level a policy issue. Insead, during he erm of he conrac, hey adap he premium amouns a regular imes (e.g. yearly), based on some prede ned medical in aion index. This pracice is used in several EU member counries (for insance, in Germany and in Belgium). This approach e cienly couneracs he sysemaic risk induced by medical in aion impacing all he policies of he porfolio in he same direcion. The reference medical index may be based on a represenaive baske of medical goods and services of which he price is followed over ime, or on indusry-wide loss daa. Besides public agencies, also privae consuling rms develop indicaors for medical insurance. See, e.g., Da Silva (2007), Devolder and Yerna (2008) and Ranjee e al. (2011). In his paper, we do no discuss he consrucion of he index bu, given a cerain medical index, we propose several premium indexing mechanisms aimed a mainaining fairness beween policyholders and insurer. The medical index considered in his paper is assumed o accoun for all sources of in aion, no only he increase in medical coss above he in aion aken ino acoun by he "usual" consumer price index. Imporan o noice is ha no only fuure premiums need o be increased o ake ino accoun he medical in aion, bu also he reserve may need o be adaped in order o resore he acuarial equivalence ha mus exis beween he liabiliies of boh parners of he insurance conrac. The remainder of his paper is organized as follows. Secion 2 discusses a premium indexing mechanism. This mehod is illusraed wih numerical examples in Secion 3. The nal secion brie y concludes. 2
3 2 Indexing for medical in aion 2.1 Bene srucure We consider healh insurance conracs wih non-ransferable reserves (ha is, he reserve is no paid ou o he insured when he lapses he conrac), as i is ypically he case on he Belgian marke. I is obvious ha he non-ransferabiliy of he reserves has a premium-reducing e ec. Hereafer, ime measures he senioriy of he policy (i.e., he ime elapsed since policy issue). Policyholder s age a policy issue is denoed by x, so ha age a ime is x +. We denoe he ulimae age by! (in case of a lifelong cover, he policy is assumed o cease a age!). The superscrip "(0)" is used o denoe quaniies deermined a policy issue. The average annual claim amoun a age x+j, j = 0; 1; 2; : : : ;! x 1, is denoed as c (0) x+j. Noice ha j refers o he ime passed since policy issue and ha he he superscrip "(0)" indicaes ha he bene s c (0) x+j are deermined a ime 0. Henceforh, we assume ha he annual claim amouns are subjec o in aion, whereas he oher elemens of he echnical basis (ineres rae, moraliy rae and lapse rae) are in line wih he realiy ha unfolds over ime (which implies ha hese elemens don have o be indexed over ime in order o mainain acuarial equilibrium). This simplifying assumpion is no realisic bu allows us o isolae and invesigae he e ec of medical in aion. 2.2 Level premiums The non-exi probabiliy k p x+ is he probabiliy ha a policy in force a age x + is sill in force k years laer, ha is, Z k kp x+ = exp x++s + x++s ds ; 0 = 1 kq [d] x+ 1 kq [w] x+ ; where x++k is he insananeous deah rae a age x + + k, while x++k is he insananeous lapse rae a he same age. The noaions k q [d] x+ and 3
4 are used o denoe he absolue raes of decremen (also called he independen probabiliies of exiing), i.e. kq [w] x+ kq [d] x+ = 1 exp Z k 0 x++s ds and k q [w] x+ = 1 exp Z k 0 x++s ds : Assuming ha he bene s are paid a he beginning of he year (a convenien and conservaive, ye unrealisic assumpion), he expeced presen value of all fuure bene s, evaluaed a policy issue, is denoed by B (0) x = 1X k=0 c (0) x+k v(0; k) kp x ; where v(s; ); s ; is he discoun facor over he period (s; ). Noice ha he sum in his expression is a nie sum, as k p x = 0 if k! x. Assuming ha level premiums of amoun (0) x are paid yearly in advance as long as he policy is in force, he acuarial equivalence principle gives rise o (0) x = B(0) x where a x = a x 1X v(0; k) k p x : Noe ha he premium calculaion is based on he expeced coss c (0) x+k evaluaed a ime 0, wihou allowance for fuure in aion. An alernaive, no sudied in he presen paper, consiss in compuing (0) x from expeced coss impaced by an assumed scenario for fuure medical in aion. The c (0) x+k framework described in his paper can be adaped o ake ino accoun such a scenario. k=0 2.3 Indexing a ime = 1 Henceforh, he superscrip "()", = 1; 2; : : :, is used o indicae ha he calculaions include medical in aion from policy issue o ime. According o he equivalence principle, he level premium (0) x is deermined such ha he iniial reserve V (0) 0 is equal o 0: V (0) 0 = B (0) x (0) x a x = 0: (1) 4
5 The bene s paid in year (0; 1) are denoed by c (0) x. As menioned before, we assume ha he observed moraliy, lapse and ineres raes follow he echnical basis assumpions. We denoe he available reserve per policy in force a ime 1 by V (0) 1. This reserve is given by V (0) 1 = (0) x c (0) x [v(0; 1) 1 p x ] Taking ino accoun he equivalence relaion (1), one can ransform his rerospecive expression for V (0) 1 ino he following prospecive expression: where and B (0) V (0) 1 = B (0) x+1 (0) x a x+1 ; x+1 = 1 P a x+1 = c (0) k=0 1 : x+1+kkp x+1 v(1; 1 + k) 1X v(1; 1 + k) k p x+1 : k=0 Hence, he available reserve a ime 1, i.e. [ (0) x c (0) x ] [v(0; 1) 1 p x ] 1, is equal o he required reserve a ime 1, i.e. B (0) x+1 (0) x a x+1, provided all assumpions concerning he echnical basis are me. Medical in aion is aken ino accoun ex-pos as i emerges over ime by adaping he premium amoun from year o year according o he procedure described hereafer. Le j [B] 1 be he medical in aion observed during he rs year. Due o his observed medical in aion, a ime 1 he expeced presen value of he fuure bene s B (0) x+1 has o be replaced by B (1) x+1 = (1 + j [B] 1 )B (0) x+1: Noe ha we assumed ha he yearly expeced coss a all ages are impaced equally by he medical in aion, i.e. he ideniy c (1) x+ x+ is = (1 + j [B] 1 )c (0) assumed o hold for all. An alernaive, no sudied in he presen paper, is ha medical in aion depends on age. I is a raher sraighforward exercise o adap he ex-pos premium indexing mechanism ha we presen hereafer o he siuaion wih age-dependen medical in aion. Due o he observed medical in aion, we nd ha V (0) 1 6= (1 + j [B] 1 )B (0) x+1 (0) x a x+1 ; 5
6 which means ha he acuarial equivalence is broken, i.e. he available reserve is di eren from he required reserve. To resore he acuarial equivalence, he insurer has o adap he premiums and/or reserve for his conrac. Suppose ha he level premium (0) x is from ime 1 on replaced by (1) x, while he available reserve V (0) 1 a ime 1 is changed ino V (1) 1. The proporional increases of he premium and he reserve are denoed by j [P ] 1 and j [V ] 1, respecively, ha is, (1) x = (1 + j [P ] 1 ) (0) x and V (1) 1 = (1 + j [V ] 1 )V (0) 1 : Following Piacco (1999), j [P ] 1 and j [V ] 1 are chosen such ha he acuarial equivalence is resored a ime 1, i.e. such ha or, equivalenly, (1 + j [V ] 1 )V (0) 1 = (1 + j [B] 1 )B (0) x+1 (1 + j [P ] 1 ) (0) x a x+1 ; V (1) 1 = B (1) x+1 (1) x a x+1 : This means ha he available reserve a ime 1, i.e. V (1) 1 is equal o he required reserve a ime 1, i.e. B (1) x+1 (1) x a x+1. From ime 1 on, he original level premiums (0) x ha were deermined a policy issue, are replaced by new level premiums (1) x. Noice ha he premium increases j [P ] 1 (0) x are nanced by he policyholder, while he reserve increase j [V ] 1 V (0) 1 is nanced by he insurer. In pracice, he insurer may nance he reserve increase, parially or fully, from echnical gains on ineres, moraliy and lapses. 2.4 Indexing a ime = 2; 3; : : : Le us now suppose ha we are a ime, = 2; 3; : : :. Reevaluaions up o ime 1 have lead o ( 1) c x++k = c (0) ( 1) B x+ = 1 P k=0 ( 1) x = Q 1 h=1 x++k h=1 ( 1) c Q 1 (1 + j [B] ); k = 0; 1; : : : ; x++kkp x+ v(; + k); (1 + j [P ] h h )(0) x : 6
7 A each ime 1; 2; : : : ; 1, he available reserve and he premium have been rese such ha available and required reserve are equal. In paricular, a ime ( 1) ( 1) 1, he available reserve V 1 and he premium x have been rese such ha ( 1) ( 1) ( 1) V 1 = B x+ 1 x a x+ 1 : (2) The reserve available a ime for a person aged x a policy issue, aking ino accoun all informaion unil ime 1, is hen given by h i ( 1) ( 1) ( 1) ( 1) V = V 1 + [v( 1; ) 1 p x+ 1 ] 1 : x c x Taking ino accoun (2), he following prospecive expression can be derived for he available reserve: ( 1) V = B ( 1) ( 1) x+ x a x+ : Le j [B] be he medical in aion observed during he year ( 1; ). Therefore, a ime we have o replace B ( 1) by x+ B () x+ = (1 + j [B] )B ( 1) x+ : The acuarial equivalence is again broken, in he sense ha he available reserve is no equal o he required reserve: V ( 1) 6= (1 + j [B] )B ( 1) ( 1) x+ x a x+ : In order o resore he acuarial equivalence, he premium and reserve are adaped o () x = (1 + j [P ] ) ( 1) x and V () = (1 + j [V ] )V ( 1) ; such ha he available reserve and he required reserve are equal: (1 + j [V ] )V or, equivalenly, ( 1) = (1 + j [B] ( 1) )B x+ (1 + j [P ] ( 1) ) x a x+ ; (3) V () = B () x+ () x a x+ : The acuarial equivalence may be resored by an in nie number of pairs j [V ] ; j [P ]. When j [V ] = 0, he bene increase is compleely paid by he policyholder. On he oher hand, choosing j [P ] increase is compleely nanced by he insurer. 7 = 0 means ha he bene
8 2.5 Relaionships beween j [B], j [V ] and j [P ] The bene in aion j [B] is equal o a weighed arihmeic average of j [V ], wih weighs ha sum up o 1, ha is, j [P ]! = V ( 1) ( 1) B j [B] x+ j [V ] + ( 1) x a x+ ( 1) B x+ This relaionship beween j [B], j [V ] and j [P ] acuarial equivalence condiion (3).! and j [P ] : (4) follows immedialy from he The equilibrium resoring procedure, expressed by (3) or equivalenly by (4), applied on a conrac per conrac basis, is an acuarial sound sysem (provided he assumpions we made are me). Noice however ha before he procedure can be applied in pracice, a choice has o be made abou how he addiional cos arising from he unanicipaed in aion is shared beween he policyholder and he insurer. A simple and ransparan rule, unambigously described in he policy condiions, is appropriae here. Taking ino accoun ha we assumed ha, apar from he in aion, all assumpions made in he echnical basis are me, i may be reasonable o se j [V ] = 0, implying ha he insured nances he increased fuure bene s. The premium increase j [P ] can hen be deermined on a yearly basis from he equilibrium condiion (3). A problem wih he procedure explained above is ha he premium increases j [P ] may ucuae heavily from year o year. Therefore, we propose a more sable procedure. In paricular, le us assume ha he policy sipulaes ha he yearly premium increase j [P ] is given by j [P ] = (1 + ) j [B] ; = 1; 2; : : : (5) for some xed value of. Suppose e.g. ha = 0:5, hen a medical in aion of 4% will lead o a premium increase of 6%. The exra increase j [B] over he bene in aion j [B] can be inerpreed in erms of he policyholder s conribuion o he reevaluaion of he reserve. Taking ino accoun (4) and (5), we nd he following resuls for he case where he premium increase is se equal o he bene increase: = 0 ) j [P ] = j [V ] = j [B] : 8
9 Hence, in case he proporional premium increase is chosen equal o he proporional bene increase, we nd ha he reserve has o be increased by he same proporion in order o resore he acuarial equivalence. Also, > 0 ) j [P ] < 0 ) j [P ] > j [B] and j [V ] < j [B] ; < j [B] and j [V ] > j [B] : This means ha if he proporional premium increase is se larger (respecively smaller) han he proporional bene increase, hen he required proporional increase of he reserve is lower (respecively higher) han he bene- increase. Taking ino accoun our assumpion ha here are no echnical gains, a sricly posiive value of will be appropriae. From equaion (4) i follows ha he relaive required reserve increase j [V ] is a decreasing funcion of = j [P ] j [B] =j [B]. 2.6 A sable premium indexing mechanism The advanage of a premium indexing mechanism of he form (5) is ha i makes he relaive increase of he premium over ime more sable.the value of in (5) could be xed in he policy. Alernaively, i could be deermined on a regular basis (e.g. every couple of years) according o a well-speci ed procedure, or i could be provided by he regulaor on a regular basis. The choice of a fair value of is crucial. If is oo low, he insurer will have o nance he fuure increases of he reserves himself. On he oher hand, if is oo high, he policyholder will consider he insurance conrac as an unfair deal, and evenually no buy he conrac. Hereafer, we presen some possible ways o deermine he facor Opimal for a given age a policy issue To deermine an appropriae value for he facor on a single policy corresponding o he age a policy issue x, we propose o calculae he acuarial presen value of all fuure required reserve increases as AP V x () = 1X j [V ] ( 1) V =1 p x v(0; ): (6) 9
10 Thus, AP V x () expresses he acuarial value of he fuure reserve increases for his conrac. Under he appropriae assumpions, i can be inerpreed as he exra capial o be injeced by he insurer in order o fund all fuure required reserve increases. A posiive value of AP V x () poins o an acuarial loss while a negaive AP V x () is an acuarial gain on his conrac for he insurer. Taking ino accoun ha we assumed ha here emerge no echnical gains on ineres, moraliy and lapse raes, he conrac can be considered as fair for boh paries if AP V x () = 0. The opimal for a given age a policy issue, which will be denoed by x, is hen deermined by seing he expeced presen value of all fuure required reserve increases equal o 0, i.e. x is he roo of he equaion AP V x () = 0. Of course, he deerminaion of he opimal a ime 0 requires he knowledge of j [V ], = 1; 2; : : :, which correspond o he fuure medical in aion, = 1; 2; : : :, unknown a policy issue. Thus, deermining x according o j [B] he principle explained above requires an assumpion for he fuure medical in aion Opimal for a given porfolio of new enrans In general he opimal "exra premium increase facor " is dependen on he age a policy issue. Alhough from an acuarial poin of view i is possible o work wih an age-dependen x, consumers and regulaors may prefer a more sraighforward and simple approach, where he opimal is independen of he age a policy issue. Hereafer, we propose a possible way o deermine his age-independen opimal which will be denoed by. We rs de ne AP V () =! P 1 x=x 0 n x AP V x (); where x 0 is he younges age of enry and n x is he esimaed number of enrans a age x in his porfolio. Hence, AP V () expresses he acuarial value of he fuure reserve increases for his porfolio of new enrans. A posiive value of AP V () corresponds o an acuarial loss, while a negaive value of AP V () is an acuarial gain on his porfolio for he insurer. The opimal value of, which will be denoed by, is hen deermined as 10
11 he roo of he equaion AP V () = 0. Remark ha he use of an ageindependen opimal has he advanage (or disadvanage) ha i inroduces inergeneraional solidariy. Deermining according o he principle explained above again requires an assumpion for he fuure medical in aion. The numerical illusraions carried ou in he nex secion show ha several scenario s of fuure in aion lead o similar values of, indicaing ha he opimal is raher robus o he magniude of medical in aion. 3 Numerical illusraion 3.1 Technical basis In he numerical examples, he discoun facors correspond o a consan yearly ineres rae of 2%. The absolue rae of decremen due o deah q y [d] conforms o he rs Heligman-Pollard law, ha is, q [d] y 1 q [d] y = A (y+b)c + De E(ln y ln F )2 + GH y wih A = 0:00054, B = 0:017, C = 0:101, D = 0:00013, E = 10:72, F = 18:67, G = 1: and H = 1:11. Furhermore, we consider a lifelong cover and we x he ulimae age o! = 110. In line wih curren pracice on he Belgian marke, we assume ha he one-year absolue rae of decremen due o lapse q y [w] is equal o 0:1 0:002(y 20) a age y = 25; 26; : : : ; 70 and 0 oherwise. The lapse rae only depend on he aained age and no on he ime elapsed since policy issue. Figure 1 displays he one-year independen probabiliies q y [w] and 1 q y [d], as well as he non-exi probabiliies p y enering he compuaions. Based on healh insurance daa colleced by he Ialian Naional Insiue of Saisics (ISTAT) graduaed by he Ialian Associaion of Insurance Companies (ANIA), we choose he annual average claim amouns a age y and esimaed a ime 0, equal o c (0) y = 0: exp(0:038637y); y 20: 11
12 Figure 1: q y [w], 1 q y [d] and p y. 3.2 Iniial premium and reserves The level premium (0) x for an insured aged x a policy issue, x = 25; 26; : : : ; 70; is shown in Figure 2. The rajecory of he non-ransferable reserves for a policyholder aged 25 a policy issue, assuming ha no medical in aion is occurring during he erm of he conrac, is shown in Figure 3. Figure 2: Level premiums (0) x for di eren ages. 12
13 Figure 3: Reserves V (0) for a person aged 25 a policy issue when j [B] = Opimal as a funcion of he age a enry Figure 4 displays he expeced presen value of all fuure reserve increases AP V 25 () as a funcion of for 3 di eren scenario s of a consan in aion over ime: j [B] = 2:5%; 4% and 6%, respecively, while j [P ] = (1+)j [B] for all. Obviously, for a given in aion scenario, AP V 25 () is a decreasing funcion of : he higher, he more he policyholder nances he bene increases himself. Furher, for a given value of, he funcion AP V 25 () is an increasing funcion of he level of in aion: a higher level of he in aion leads o higher required reserve increases. For he scenario where j [B] = 2:5%, he opimal 25 lies beween 0:6 and 0:7. Increasing he yearly medical in aion o 4% or 6% leads o a seeper decreasing funcion AP V 25 () and decreases he value of he opimal value 25. The opimal 25 urns ou o be a decreasing funcion of he assumed medical in aion. The previous calculaions have been repeaed for all ages x a policy issue beween 20 and 70. The opimal values x, for he hree scenarios of medical in aion (j [B] = 2:5%; j [B] = 4% and j [B] = 6%), are depiced in Figure 5. The opimal facor x is a decreasing funcion of age x a policy issue. This is due o he shorer remaining period of he conrac and he fac ha he premium is an incrasing funcion of age a policy issue. From Figure 5, i is also clear ha for older ages x, he bene increase facor j [B] has a raher moderae e ec on he opimal facor x. The explanaion for his observaion lies again in he shorer remaining erm of he conrac. 13
14 Figure 4: AP V 25 () when j [P ] = (1 + )j [B]. Figure 5: The opimal facor x as a funcion of age a policy issue. 3.4 Opimal for a porfolio of new enrans Le us suppose ha he age of new enrans in a given year is disribued as shown in Figure 6. This disribuion is based on Belgian daa. The high number of new enrans a age 20 is due o he fac ha conracs for ages younger han 20 are yearly renewable and priced on a risk premium basis, while he level premium srucure wih indexaion as described above is only applied from age 20 onwards. The acuarial presen value of he fuure reserve increases AP V () as a funcion of he facor is given in Figure 7 for hree scenarios of medical in aion (j [B] = 2:5%; j [B] = 4% and j [B] = 6%). We observe ha for a given 14
15 in aion scenario, AP V () is a decreasing funcion of, while for a given value of, he funcion AP V 25 () is an increasing funcion of he level of in aion. For j [B] = 2:5%, he opimal lies beween 0:4 and 0:5. Increasing he yearly medical in aion o 4% or 6% leads o a seeper decrease of he funcion AP V () and decreases he value of he opimal value. Despie his decreasing e ec, he high of he medical in aion seems o have only a moderae e ec on he opimal value. Figure 6: Disribuion of he age of new enrans. Figure 7: AP V () as a funcion of in case j [P ] = (1 + )j [B]. 15
16 4 Conclusion In his paper, we considered lifelong healh insurance conracs, wih level premiums ha are se up a policy issue, no aking ino accoun fuure (upredicable) medical in aion. We propose some premium indexing mechanisms which yearly resore he acuarial equivalence, aking ino accoun he observed medical in aion over he pas year. Firs, we discussed he general relaion ha has o hold beween yearly bene, premium and reserve increases in order o accoun for he unanicipaed in aion ha has occured. This equaion can in principle be used as he basis for indexing he premiums on a policy per policy and year o year basis, implying ha he relaive premium increase is a funcion of age a policy and of he number of years ha he policy is in force. Nex, we invesigaed a framework where he premium amoun is supposed o be yearly impaced by he observed medical in aion muliplied wih a facor (1 + ) for some > 0 which is chosen upfron. The proposed opimal value for for a given age x a policy issue is hen chosen such ha he acuarial value of all fuure required reserve increases of he conrac is equal o 0. This individual approch is supposed o make he yearly relaive premium increases above he observed medical in aion more sable. Finally, we proposed an aggregae approach which is applicable o a whole porfolio of new enrans, where an overall opimal is deermined. The laer approach leads o age-independen relaive premium increases above he medical in aion. Hence, i inroduces inergeneraional solidariy in he considered porfolio. Throughou he paper, we have assumed ha reserves are no ransferable, which is in line wih producs currenly o ered on he Belgian marke. Allowing for fully or parially ransferable reserves is a opic for fuure research. Noe ha he indexing mechanisms described in he presen paper may also apply o oher long erm life and healh insurance producs. In life insurance for insance, adapaion o a changing moraliy paern can be performed in a similar way, de ning appropriae moraliy indices. This approach, which is an e cien hedge for sysemaic longeviy risk, which is inheren in aging populaions, is also a opic for fuure research. Acknowledgemen 16
17 We would like o hank AG Insurance for he nancial suppor via he Chair on Healh Insurance a KU Leuven. References Da Silva, R. (2007). Indexaion of medical coss for Souh African medical Schemes. IAAHS Colloquium, Cape Town, May Devolder, P., Yerna, B.-L. (2008). Consrucion d une méhode spéci que d indexaion des conras privés d assurance maladie. Belgian Acuarial Bullein 8, Piacco, E. (1999). Mulisae models for long-erm care insurance and relaed indexing problems. Applied Sochasic Models in Business and Indusry 15, Ramjee, S., Kooverjee, A., Dreyer, K. (2011). The consrucion of a price index for Souh African medical scheme conribuions. Acuarial Sociey of Souh Africa s 2011 Convenion, Johannesburg, November
PREMIUM INDEXING IN LIFELONG HEALTH INSURANCE
Far Eas Journal of Mahemaical Sciences (FJMS 203 Pushpa Publishing House, Allahabad, India Published Online: Sepember 203 Available online a hp://pphm.com/ournals/fms.hm Special Volume 203, Par IV, Pages
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationIndividual Health Insurance April 30, 2008 Pages 167-170
Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationLongevity 11 Lyon 7-9 September 2015
Longeviy 11 Lyon 7-9 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univ-lyon1.fr
More informationUNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert
UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of Erlangen-Nuremberg Lange Gasse
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More informationFifth Quantitative Impact Study of Solvency II (QIS 5) National guidance on valuation of technical provisions for German SLT health insurance
Fifh Quaniaive Impac Sudy of Solvency II (QIS 5) Naional guidance on valuaion of echnical provisions for German SLT healh insurance Conens 1 Inroducion... 2 2 Calculaion of bes-esimae provisions... 3 2.1
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:
More informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationLife insurance cash flows with policyholder behaviour
Life insurance cash flows wih policyholder behaviour Krisian Buchard,,1 & Thomas Møller, Deparmen of Mahemaical Sciences, Universiy of Copenhagen Universiesparken 5, DK-2100 Copenhagen Ø, Denmark PFA Pension,
More informationA Re-examination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationTHE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS
VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More informationOn the Management of Life Insurance Company Risk by Strategic Choice of Product Mix, Investment Strategy and Surplus Appropriation Schemes
On he Managemen of Life Insurance Company Risk by raegic Choice of Produc Mix, Invesmen raegy and urplus Appropriaion chemes Alexander Bohner, Nadine Gazer, Peer Løche Jørgensen Working Paper Deparmen
More informationThe Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees.
The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling 1 Insiu für Finanz- und Akuarwissenschafen, Helmholzsraße 22, 89081
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationThe Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees
1 The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling Insiu für Finanz- und Akuarwissenschafen, Helmholzsraße 22, 89081
More informationA Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk Jensen, Ninna Reitzel; Schomacker, Kristian Juul
universiy of copenhagen Universiy of Copenhagen A Two-Accoun Life Insurance Model for Scenario-Based Valuaion Including Even Risk Jensen, Ninna Reizel; Schomacker, Krisian Juul Published in: Risks DOI:
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationWorking Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits
Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion
More informationNiche Market or Mass Market?
Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationTHE IMPACT OF THE SECONDARY MARKET ON LIFE INSURERS SURRENDER PROFITS
THE IPACT OF THE ECONDARY ARKET ON LIFE INURER URRENDER PROFIT Nadine Gazer, Gudrun Hoermann, Hao chmeiser Insiue of Insurance Economics, Universiy of. Gallen (wizerland), Email: nadine.gazer@unisg.ch,
More informationMarkov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension
Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension Lars Frederik Brand Henriksen 1, Jeppe Woemann Nielsen 2, Mogens Seffensen 1, and Chrisian Svensson 2 1 Deparmen of Mahemaical
More informationABSTRACT KEYWORDS. Term structure, duration, uncertain cash flow, variable rates of return JEL codes: C33, E43 1. INTRODUCTION
THE VALUATION AND HEDGING OF VARIABLE RATE SAVINGS ACCOUNTS BY FRANK DE JONG 1 AND JACCO WIELHOUWER ABSTRACT Variable rae savings accouns have wo main feaures. The ineres rae paid on he accoun is variable
More informationOptimal Longevity Hedging Strategy for Insurance. Companies Considering Basis Risk. Draft Submission to Longevity 10 Conference
Opimal Longeviy Hedging Sraegy for Insurance Companies Considering Basis Risk Draf Submission o Longeviy 10 Conference Sharon S. Yang Professor, Deparmen of Finance, Naional Cenral Universiy, Taiwan. E-mail:
More informationHow To Calculate Price Elasiciy Per Capia Per Capi
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationAnalyzing Surplus Appropriation Schemes in Participating Life Insurance from the Insurer s and the Policyholder s Perspective
Analyzing Surplus Appropriaion Schemes in Paricipaing Life Insurance from he Insurer s and he Policyholder s Perspecive Alexander Bohner, Nadine Gazer Working Paper Chair for Insurance Economics Friedrich-Alexander-Universiy
More information11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge
More informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
More informationDOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios
More informationChapter 7. Response of First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationIMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION. Tobias Dillmann * and Jochen Ruß **
IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION Tobias Dillmann * and Jochen Ruß ** ABSTRACT Insurance conracs ofen include so-called implici or embedded opions.
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationAn Optimal Strategy of Natural Hedging for. a General Portfolio of Insurance Companies
An Opimal Sraegy of Naural Hedging for a General Porfolio of Insurance Companies Hong-Chih Huang 1 Chou-Wen Wang 2 De-Chuan Hong 3 ABSTRACT Wih he improvemen of medical and hygienic echniques, life insurers
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures
More informationThis page intentionally left blank
This page inenionally lef blank Marke-Valuaion Mehods in Life and Pension Insurance In classical life insurance mahemaics, he obligaions of he insurance company owards he policy holders were calculaed
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More informationSPEC model selection algorithm for ARCH models: an options pricing evaluation framework
Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationModeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling
Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
This documen is downloaded from DR-NTU, Nanyang Technological Universiy Library, Singapore. Tile A Bayesian mulivariae risk-neural mehod for pricing reverse morgages Auhor(s) Kogure, Asuyuki; Li, Jackie;
More informationThe Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies
1 The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling * Insiu für Finanz- und Akuarwissenschafen, Helmholzsr. 22, 89081 Ulm, Germany
More informationCLASSIFICATION OF REINSURANCE IN LIFE INSURANCE
CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly
More informationAppendix D Flexibility Factor/Margin of Choice Desktop Research
Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationBasic Life Insurance Mathematics. Ragnar Norberg
Basic Life Insurance Mahemaics Ragnar Norberg Version: Sepember 22 Conens 1 Inroducion 5 1.1 Banking versus insurance...................... 5 1.2 Moraliy............................... 7 1.3 Banking................................
More informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
More informationRationales of Mortgage Insurance Premium Structures
JOURNAL OF REAL ESTATE RESEARCH Raionales of Morgage Insurance Premium Srucures Barry Dennis* Chionglong Kuo* Tyler T. Yang* Absrac. This sudy examines he raionales for he design of morgage insurance premium
More informationThe Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
More informationLECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE:
LECTURE: SOCIAL SECURITY HILARY HOYNES UC DAVIS EC230 OUTLINE OF LECTURE: 1. Inroducion and definiions 2. Insiuional Deails in Social Securiy 3. Social Securiy and Redisribuion 4. Jusificaion for Governmen
More informationON THE PRICING OF EQUITY-LINKED LIFE INSURANCE CONTRACTS IN GAUSSIAN FINANCIAL ENVIRONMENT
Teor Imov r.amaem.sais. Theor. Probabiliy and Mah. Sais. Vip. 7, 24 No. 7, 25, Pages 15 111 S 94-9(5)634-4 Aricle elecronically published on Augus 12, 25 ON THE PRICING OF EQUITY-LINKED LIFE INSURANCE
More informationChapter Four: Methodology
Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationDefault Risk in Equity Returns
Defaul Risk in Equiy Reurns MRI VSSLOU and YUHNG XING * BSTRCT This is he firs sudy ha uses Meron s (1974) opion pricing model o compue defaul measures for individual firms and assess he effec of defaul
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces ime-series smoohing forecasing mehods. Various models are discussed,
More informationOptimal Stock Selling/Buying Strategy with reference to the Ultimate Average
Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July
More informationThe Economic Value of Medical Research
The Economic Value of Medical Research Kevin M. Murphy Rober Topel Universiy of Chicago Universiy of Chicago March 1998 Revised Sepember, 1999 Absrac Basic research is a public good, for which social reurns
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationRelationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**
Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationDouble Entry System of Accounting
CHAPTER 2 Double Enry Sysem of Accouning Sysem of Accouning \ The following are he main sysem of accouning for recording he business ransacions: (a) Cash Sysem of Accouning. (b) Mercanile or Accrual Sysem
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationTHE DETERMINATION OF PORT FACILITIES MANAGEMENT FEE WITH GUARANTEED VOLUME USING OPTIONS PRICING MODEL
54 Journal of Marine Science and echnology, Vol. 13, No. 1, pp. 54-60 (2005) HE DEERMINAION OF POR FACILIIES MANAGEMEN FEE WIH GUARANEED VOLUME USING OPIONS PRICING MODEL Kee-Kuo Chen Key words: build-and-lease
More informationDEMAND FORECASTING MODELS
DEMAND FORECASTING MODELS Conens E-2. ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysem-level Model Couny-level Model Easside King Couny-level Model E-6. ELECTRIC PEAK HOUR LOAD FORECASTING Sysem-level Forecas
More informationPricing Fixed-Income Derivaives wih he Forward-Risk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK-8 Aarhus V, Denmark E-mail: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs
More informationSingle-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1
Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationEfficient Risk Sharing with Limited Commitment and Hidden Storage
Efficien Risk Sharing wih Limied Commimen and Hidden Sorage Árpád Ábrahám and Sarola Laczó March 30, 2012 Absrac We exend he model of risk sharing wih limied commimen e.g. Kocherlakoa, 1996) by inroducing
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationA Conceptual Framework for Commercial Property Price Indexes
Gran-in-Aid for Scienific Research(S) Real Esae Markes, Financial Crisis, and Economic Growh : An Inegraed Economic Approach Working Paper Series No.4 A Concepual Framework for Commercial Propery Price
More informationSome Quantitative Aspects of Life Annuities in Czech Republic
Some Quaniaive Aspecs of Life Annuiies in Czech Republic Tomas Cipra The conribuion deals wih some quaniaive aspecs of life annuiies when applied in he Czech Republic. In paricular, he generaion Life Tables
More informationOptimal Consumption and Insurance: A Continuous-Time Markov Chain Approach
Opimal Consumpion and Insurance: A Coninuous-Time Markov Chain Approach Holger Kraf and Mogens Seffensen Absrac Personal financial decision making plays an imporan role in modern finance. Decision problems
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUN-SHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 6-7 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUN-SHAN WU Deparmen of Bussines Adminisraion
More informationDynamic Hybrid Products in Life Insurance: Assessing the Policyholders Viewpoint
Dynamic Hybrid Producs in Life Insurance: Assessing he Policyholders Viewpoin Alexander Bohner, Paricia Born, Nadine Gazer Working Paper Deparmen of Insurance Economics and Risk Managemen Friedrich-Alexander-Universiy
More informationRecovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures
w o r k i n g p a p e r 5 7 Recovering Marke Expecaions of FOMC Rae Changes wih Opions on Federal Funds Fuures by John B. Carlson, Ben R. Craig, and William R. Melick FEDERAL RESERVE BANK OF CLEVELAND
More informationPremium Income of Indian Life Insurance Industry
Premium Income of Indian Life Insurance Indusry A Toal Facor Produciviy Approach Ram Praap Sinha* Subsequen o he passage of he Insurance Regulaory and Developmen Auhoriy (IRDA) Ac, 1999, he life insurance
More informationAnnuity Decisions with Systematic Longevity Risk
Annuiy Decisions wih Sysemaic Longeviy Risk Ralph Sevens This draf: November, 2009 ABSTRACT In his paper we invesigae he effec of sysemaic longeviy risk, i.e., he risk arising from uncerain fuure survival
More informationCOPING WITH REVENUE RECOGNITION IN THE LOYALTY REWARD PROGRAMS INDUSTRY: A STOCHASTIC MODELING APPROACH
AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 COPING WITH REVENUE RECOGNITION IN THE LOYALTY REWARD PROGRAMS INDUSTRY A STOCHASTIC MODELING APPROACH
More informationFair Valuation and Risk Assessment of Dynamic Hybrid Products in Life Insurance: A Portfolio Consideration
Fair Valuaion and Risk ssessmen of Dynamic Hybrid Producs in ife Insurance: Porfolio Consideraion lexander Bohner, Nadine Gazer Working Paper Deparmen of Insurance Economics and Risk Managemen Friedrich-lexander-Universiy
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationAnalysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer
Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of
More informationThe Interaction of Public and Private Insurance: Medicaid and the Long-Term Care Insurance Market
The Ineracion of Public and Privae Insurance: Medicaid and he Long-Term Care Insurance Marke Jeffrey R. Brown Universiy of Illinois and NBER Amy Finkelsein MIT and NBER Ocober 2006 Absrac: This paper shows
More information