EXAMPLE EXAMPLE EXAMPLE EXAMPLE 4 UNIVERSAL TRADITIONAL APPROACH EXAMPLE 5 FLEXIBLE PRODUCT... 26
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2 EXAMLE... A. Edowme... B. ure edowme d Term surce... 4 C. Reseres Bruo premum d reseres... EXAMLE A. Whoe fe... 4 B. Reseres of Whoe fe... 6 C. Bruo Whoe fe... 7 EXAMLE A.ure edowme... 8 B. eferred uy... 8 C. Fed premum uy Reseres EXAMLE 4 UIVERSAL TRAITIOAL AROACH EXAMLE 5 FLEXIBLE ROUCT A. Cp ue he ed of pocy B. Mmzg premum C. Edowme EXAMLE 6 CASH-FLOW MOEL A. rofby es B. Lby Adequcy Tes... 3 ACTUARIAL FORMULAS A MS EXCEL FUCTIOS... 3 omecure... 3 Mory bes d Commuo bes... 3
3 Acur fucos Reseres Regur eo premum TUTORIAL OF MS EXCEL ALICATIO... 38
4 Empe A ce, m 25 yers od, ws o me surce corc for 25 yers. A. I cse of deh he ws o secure hs fmy wh 2. I cse he w sure 25 yers he so ws o recee 2. How much woud hs d of corc cos hm ow? ere resus sge premum d regur premum for eery sge yer d eery sge moh. B. The ce ws o see how much of he premum he pys for surce o secure hs fmy cse of deh d how much for 2 cse he sures. ere resus sge d regur premum. C. You, s surce compy, shoud be be o coer mos of your corcs. For h purpose you shoud ccue reseres for cosdered corcs. Ccue resere yer 7.. Appy chrges d ccue bruo premum d reseres of corcs meoed seco A d B. *oe: ssume rdo pproch wh eres re.25 p.. A. Edowme Geder Me Age 25 ocy perod 25 eh beef (K) 2 Sur beef () 2 Ieres re ().25 Type of surce corc Edowme remum: Edowme Sge 8 888,99 Regur u 5 828,87 Regur mohy 493,63 Sge premum Usg Ece fuco Usg Mory bes = K * d * + d + * d +- * + * + * 8 888,99 = 2 * 2626, ,86 *, * 98982, ,34
5 Usg probby = K * q * + q * q * + * p * 8 888,99 = 2 *, *,967 *,53939 Usg Commuo umbers = K * C + C + + C C +- + * ,99 = 2 * 46, , + 2 * 5339,5 5339,5 = K * M - M + + * ,99 = 2 * 46, , + 2 * 5339,5 5339,5 Regur premum u Usg Ece fuco Usg Acur formus = 5 829,87 = Usg probby K * A + * E ӓ 2 *, *,579 8,68 = 5 829,87 = K * q * + q * q * + * p * + p * p * - 2 *, *,579 8,68 2
6 Usg Commuo umbers = 5 829,87 = K * M - M + + * * 46, * 2765, 99728,2 = 5 829,87 = K * d * + d + * 2 + d +- * + * + * + + * + +2 * * - 2 * 2626, * 5263, ,26 Regur premum mohy Frequecy of premum (m) mohy m = 2 (m) = Regur eo premum m * ( - (m-) * ) 2m * 493,63 = 5 829,875,8 3
7 B. ure edowme d Term surce Geder Me Age 25 ocy perod 25 eh beef (K) 2 Sur beef () 2 Ieres re ().25 Type of surce corc Edowme / Term surce remum: Edowme ure edowme Term surce Sge 8 888, ,3 5 37,67 Regur u 5 828, ,7 284,7 Regur mohy 493,63 469,57 24,6 ure edowme sge premum Usg Ece fuco Usg Mory bes = * + * 3 58,3 = 2 * 9539,86 *, ,34 Usg probby = * p * 3 58,3 = 2 *,967 *,53939 Usg Commuo umbers = * ,3 = 2 * 2765, 5339,5 4
8 ure edowme Regur premum uy Usg Ece fuco Usg Acur formus = * 5 545,7 = 2 * E ӓ,579 8,68 Usg Commuo umbers = * 5 545,7 = 2 * , 99728,2 Usg Mory bes = * 5 545,7 = 2 * + * + + * + +2 * * , ,26 Usg probbes = * 5 545,7 = 2 * p * + p * p * -,579 8,68 5
9 ure edowme Regur premum mohy Frequecy of premum (m) mohy m = 2 Regur eo premum (m) = m * ( - (m-) * ) 2m * 469,57 = 5 545,7,8 Term surce Sge premum Usg Ece fuco: Usg Mory bes = K * d * + d + * 2 + d +- * 5 37,67 = 2 * Usg probbes 2626, ,34 = K * q * + q * q * 5 37,67 = 2 *,2654 Usg Commuo umbers = K * C + C + + C +2 + C +- = M - M ,67 = 2 * 46,89 46,89 = 5339,5 5339,5 6
10 Term surce Regur premum uy Usg Ece fuco Usg Acur formus = K * 284,7 = 2 * A ӓ,2654 8,68 Usg Commuo umbers = K * M - M + = C + C + + C +2 + C ,7 = 2 * 46,89 46,89 = 99728, ,2 Usg Mory bes = K * 284,7 = 2 * d * + d + * 2 + d +- * + + * + +2 * * , ,26 Usg probbes = K * 284,7 = 2 * q * + q * q * + p * p * -,2654 8,68 Term surce Regur premum - mohy Frequecy of premum (m) mohy m = 2 Regur eo premum (m) = m * ( - (m-) * ) 2m * 24,6 = 284,7,8 7
11 C. Reseres Geder Me Age 25 ocy perod 25 eh beef (K) 2 Sur beef () 2 Ieres re ().25 Resere yer () 7 Type of surce corc Edowme / Term surce / ure edowme remum: Edowme Usg Ece fuco Resere of regur premum Edowme,2255*2 =44 ure edowme,257*2 =43 34 Term surce,54*2 = 8 Usg Acur formus V = A +,- - * ӓ +,-,2255 =, ,295 * 4,56 Usg Commuo umbers V = - + * ,2255 = , ,57 * 4468, ,2 2 Kč Kč 8 Kč 6 Kč 4 Kč 2 Kč Kč eo reseres
12 ure edowme Usg Ece fuco Usg Acur formus V = -E + - * ӓ +,-,257 =,6886 -,2773 * 4,56 Usg Commuo umbers V = + + * ,257 = 2765, ,63 * 4468, ,2 2 Kč Kč 8 Kč 6 Kč 4 Kč 2 Kč Kč eo reseres Term surce Usg Ece fuco: Usg Acur formus V = A +,- - * ӓ +,-,54 =,26 -,4 * 4,5584 9
13 Usg Commuo umbers V =,54 = M + - M + M - M * ,439 46, , * 4468, , ,23 2 Kč Kč 8 Kč 6 Kč 4 Kč 2 Kč Kč eo reseres
14 . Bruo premum d reseres Geder Me Age 25 ocy perod 25 eh beef (K) 2 Sur beef () 2 Ieres re ().25 Resere yer () 7 Type of surce corc Edowme / Term surce / ure edowme remum: Regur bruo Bruo resere Edowme 5 965, ,92 ure edowme 5 68, ,95 Term surce 42,92-487,7 *oe: There re o Ece fucos o ccue bruo premum Edowme Edowme bruo premum B = K * A + K + f + ӓ * f + K + f + K ) ӓ * ( - B - B ) - B 5 965,93 = 8888, , + 8,68 *,2 8,68 *,9969 -,2 Edowme bruo resere K*V bruo = K* V eo - ( K + f + B ) * ӓ +,- ӓ, ,92 = 449,87-25,9 * 4,56 8,68 Bruo reseres K*Veo K*VBruo 25 Kč 2 Kč 5 Kč Kč 5 Kč Kč -5 Kč
15 ure edowme ure edowme bruo premum * E + K + f + ӓ * f + K + f + K ) B = ӓ * ( - B - B ) - B 5 68,87 = 358,3 + 24, + 8,68 *,2 8,68 *,9969 -,2 ure edowme eo resere K* V bruo = K* V eo - ( K + f + B ) * ӓ +,- ӓ, 4 47,95 = 43 34,85-25,4 * 4,56 8,68 25 Kč Bruo reseres K*Veo K*VBruo 2 Kč 5 Kč Kč 5 Kč Kč -5 Kč
16 Term surce Term surce bruo premum B = K * A + K + f + ӓ * f + K + f + K ) ӓ * ( - B - B ) - B 42,92 = 537, , + 8,68 *,2 8,68 *,9969 -,2 Term surce bruo resere V bruo = V eo - ( K + f + B ) * ӓ +,- ӓ, -487,7 = 75, - 24,8 * 4,56 8,68 3 Kč Bruo reseres K*Veo K*VBruo 2 Kč Kč Kč - Kč -2 Kč -3 Kč
17 Empe 2 5 yers od feme ws o be sured for oe mo cse of deh. A. Compre sge d regur premum for whoe fe. B. Ccue so resere ge 75. C. Ccue whoe fe premum d resere cudg chrges. A. Whoe fe Geder Feme Age 5 ocy perod eh beef (K) Type of surce corc Whoe fe remum: Sge premum Regur premum Whoe fe , ,98 Whoe fe sge premum Usg Ece fuco: Usg Mory bes = K * d * + d + * ,44 = * Usg probby 4429, ,8 = K * q * + q * q * ,44 = *,45369 Usg commuo umbers = K * C + C + + C = M ,44 = * 2886,6 2886,6 = 2843,7 2843,7 4
18 Whoe fe Regur premum Usg Ece fuco: Usg Acur formus = K * 2 254,98 = * A ӓ, ,3988 Usg Mory bes = K * 2 254,98 = * d * + d + * * + +2 * * , ,82 Usg probbes = K * 2 254,98 = * q * + q * p * p * -,45 22,4 Usg Commuo umbers = K * M = C + C + + C ,98 = * 2886,6 2886,6 = 63697, ,45 5
19 B. Reseres of Whoe fe Geder Feme Age 5 ocy perod eh beef (K) Sur beef () Resere () 25 Type of surce corc Whoe fe remum: Resere Whoe fe,53529*m = Whoe fe Resere Usg Ece fuco: Usg Acur formus V = A + - * ӓ +,53529 =,7462 -,225 *,49 Usg Commuo umbers V = - + * +,53529 = , ,26 * 2285, ,45 2 Kč eo reseres Kč 8 Kč 6 Kč 4 Kč 2 Kč Kč
20 C. Bruo Whoe fe Geder Feme Age 5 ocy perod eh beef (K) Resere () 25 Type of surce corc Whoe fe remum: Regur bruo premum Bruo resere Whoe fe 2 443, ,79 Whoe fe Regur bruo premum Whoe fe bruo premum B = K * A + K + f + ӓ * f + K + f + K ) ӓ * ( - B - B ) - B 2 443,72 = , , + 22,4 * 35, 22,4 *,9969 -,2 Whoe fe Bruo resere Whoe fe bruo resere K * V bruo = K * V eo - ( K + f + B ) * ӓ + ӓ ,79 = ,4-224,9 *,4 22,4 2 Kč Bruo reseres K*Veo K*VBruo Kč 8 Kč 6 Kč 4 Kč 2 Kč Kč -2 Kč
21 Empe 3 Youg m of ge 3 ws o be secured whe he reches hs 6 by cer mou of moey. A. How much he hs o py eery yer o ge wo mo whe he urs 6. B. How much he woud he o py o ge 5 eery yer for he res of fe. Compre hs premum wh premum for 5 eery yer u hs 8. C. He s sure h ow he c py m 2 per yer. Wh uy he c epec whe he urs 6 u hs deh d u hs 8?. Me he reseres of hese wo corcs yer 2 d 45. A.ure edowme Usg Acur formus = * 4 68,47 = 2 * E ӓ,4262 2,95 B. eferred uy Geder Me Age () 3 ocy perod () eferred () Auy () 5 Ieres re (),25 Type of surce corc eferred / Whoe fe / Temporry uy remum: Sge premum Regur premum Whoe fe uy 3 576,34 459,22 Temporry uy ,88 27,36 Whoe fe uy Sge premum Usg Ece fuco Usg Mory bes = * 3 576,34 = 5 * ++ * * , ,7 8
22 Usg probbes = * +p * p * ,34 = 5 * 6,2 Usg Commuo umbers = * = ,34 = 5 * , ,27 = 474, 474, Whoe fe Regur premum Usg Ece fuco Regur premum = * ӓ ӓ 459,22 = 3576,34 2,95 Temporry uy Sge premum Usg Ece fuco Usg Mory bes = * ,88 = 5 * ++ * * * 52548, ,7 9
23 Usg probbes = * +p * p * p * ,88 = 5 * 5,33 Usg Commuo umbers = * = ,88 = 5 * 25489, ,59 = 474, 474, 2
24 Temporry uy Regur premum Usg Ece fuco Regur premum = * ӓ ӓ 27,36 = 26639,88 2,95 C. Fed premum uy Whoe fe 2 2, ,95 6, Temporry uy 2 2, ,58 5,32 Ece fuco for Ece fuco for Ece fuco for 2
25 . Reseres Geder Me Age () 3 ocy perod () eferred () Auy () 5 Ieres re (),25 Type of surce corc eferred / Whoe fe / Temporry uy remum: Resere = 2 Resere = 45 Whoe fe uy 4,6*5 = 2 8 7,93*5 = Temporry uy 3,63* 5 = 8 5 3,98*5 = 9 9 Whoe fe uy eo reseres 8 Kč 7 Kč 6 Kč 5 Kč 4 Kč 3 Kč 2 Kč Kč Kč Usg Ece fuco: Usg cur symbos: K=2, V for > V = * +,- 4,6 = 8,34 -,29 * 4,3 22
26 K=45, V V = + 7,93 = 7,93 Temporry uy 7 Kč eo reseres 6 Kč 5 Kč 4 Kč 3 Kč 2 Kč Kč Kč Usg Ece fuco: Usg cur symbos: K=2, V for > V = - +,- - * +,- 3,63 = 7,26 -,25 * 4,3 K = 45, V for V = +,- 3,98 = 3,98 23
27 Empe 4 Uers Trdo pproch 3 yers od m hs ery spec demds bou hs surce corc. Whe he urs 4, he ws o be sured for cse of deh. Whe he urs 5, he ws o crese deh beef up o 2 d u hs 55 he w o recee 5 eery yer. I hs 6 he ws o ge 2 d he u hs 7 o be sured for cse of deh bu does w o py premum. Ccue eo d bruo premum d resere pocy yer 5 d 25 of hs corc. Geder Me Age () 3 ocy perod () eferred () Resere () From ge 4 o 5: eh beef (K) From ge 5 o 6: 2 From ge 6 o 7: whou pyg premum Auy () From ge 5 o 55: 5 I ge 6: 2 Ieres re (),25 Type of surce corc eferred / Term surce / Temporry uy remum: eo Bruo remum 252,88 383,73 Resere yer 5-2, ,75 Resere yer 25 27, ,37 3 Kč Reseres Veo VBruo 25 Kč 2 Kč 5 Kč Kč 5 Kč Kč -5 Kč Kč -5 Kč 24
28 The pu formo of hs pocy c be see o pcure beow. 25
29 Empe 5 Febe produc e febe corc for 35 yers od me for 3 yers. A. Wh s he cp ue he ed of pocy f he premum s 2 per yer, deh beef s d frs rsco s? B. Wh s he mm premum o he resere he ed of pocy equ o zero? C. Wh s he premum for smr corc o edowme surce where he deh beef s d Sur beef s 5? A. Cp ue he ed of pocy ocy chrcerscs Mode po: Cms: Yer 25 eh SA+CV Age uo de 35 Tech. I. re 2,5% Se M ocy chrges: SA s yer 8,% remum (u) 2 2+yers 2,% CV. de rof shre 85,% ocy yer. de Surreder fee 5,% ocy_perod 3 B. Mmzg premum Yer Age ocy Yer shre CV EoY ocy chrcerscs Modepo: Cms: Yer 25 eh SA+CV Age uo de 35 Tech. I. re 2,5% Se M ocy chrges: SA s yer 8,% remum (u) yers 2,% CV. de rof shre 85,% ocy yer. de Surreder fee 5,% ocy_perod 3 *oe: Ths Souo requres o s soer. 26
30 C. Edowme ocy chrcerscs Modepo: Cms: Yer 25 eh SA Age uo de 35 Tech. I. re 2,5% Se M ocy chrges: SA s yer 8,% remum (u) 6 2+yers 2,% CV. de rof shre 85,% ocy yer. de Surreder fee 5,% ocy_perod 3 Yer Age ocy Yer shre CV EoY
31 Empe 6 Csh-Fow mode Oe bg compy ws o sure s empoyees. I cse of deh, w be pd d f sured perso sures yers he corc w be cceed d he perso w ob es 2. A empoyees re me ge 35. A. Compre rdo d febe pproch d decde whch of he wo ypes of corc s more profbe. B. Me ccuo of Lby Adequcy Tes (LAT) for boh pproches. A. rofby es Febe pproch Ccuo of febe produc premum wh SA = d he ed CV = 2. By usg soer he mm premum s ocy chrcerscs Modepo: Cms: Yer 25 eh SA Age uo de 35 Tech. I. Re 2,5% Se M ocy chrges: SA s yer 8,% remum (u) yers 2,% CV. de rof shre 85,% ocy yer. de Surreder fee 5,% ocy_perod From Csh-Fow mode he profbe crer s cr. VL cr V remum Lby mode V CF V L V remum e L To Ergs cr -25,7% cr 2-8,8% 28
32 Trdo pproch The premum of rdo pproch of edowme corc beow eeds o be frsy ccued. Tme () Age () I force remum rsfer eh beef Sur beef Regur bruo premum 2 46,58 The prof crer c be see oupu of Csh-fow mode. Lby mode V CF V L V remum 99 7 e L To Ergs cr 5,5% cr 2 25,5% Trdo pproch seems o be more profbe for surce compy bsed o rc d so for sured perso becuse of ower premum. The reso why rdo pproch ges beer resus s bsed o ssumpos of o surreders pyoffs. If ce cces febe pocy, he recees hs cp ue djused by surreder fee. I rdo pproch we ssume o pyou whe he pocy s cceed. 29
33 B. Lby Adequcy Tes Febe pproch BE Trdo pproch BE RM FV RM FV LAT LAT Afer pressg Ccue LAT Lby dequcy es w be uomcy ccued. 3
34 Acur formus d MS Ece fucos omecure X K Age ocy perod Ieres re eh beef Sur beef Tme of resere eferred me Mory bes d Commuo bes robby of deh q Ece fuco: q () q d robby of sure p Ece fuco: p () p q p umber of g Ece fuco: () p q umber of deh d Ece fuco: d () d robby of surg yers p Ece fuco: p (,) p 3
35 32 p p robby of deh yers q Ece fuco: q (,) q p q robby of deh cer ge + q Ece fuco: _q (,) d q scoued umber of g ge Ece fuco: (,) scoued umber of deh ge Ece fuco: C (,) d C Commuo umbers of frs order Ece fuco: M (,) [2] Ece fuco: (,) C C M [2] Commuo umbers of secod order Ece fuco: S (,) S [3] Ece fuco: R (,) M C R [3]
36 33 Acur fucos ure edowme Ece fuco: E (,,) E E p E Whoe fe Ece fuco: A (,) d A M C A q A Temp surce Ece fuco: A (,,) d A M M C A q A Edowme Ece fuco: A (,,I,,K) E K A A / K d A /
37 34 K M M K C A / / p K q A / Whoe fe uy Ece fuco: (,,_rerrs,frequecy,deferred) p p Temp uy Ece fuco: (,,,_rerrs,frequecy,deferred) p
38 35 p Reseres Edowme resere Ece fuco: V_ Edowme (,,) z A V,, V Whoe fe resere Ece fuco: V_ Whoe_e (,) z A V V Temp surce resere Ece fuco: V_ Temp_surce (,,) z A V,, M M M M V ure edowme reseres Ece fuco: V_ ure_edowme (,,) z E V, V eferred fe uy reseres Ece fuco:
39 36 For < V, V For >= V V Regur eo premum ure edowme regur Ece fuco: regur_ure_edowme (,,) E p p Whoe fe regur Ece fuco: regur_whoe_fe (,,) A C M d
40 37 p q Temp surce regur Ece fuco: regur_eo_temp_surce (,,) A C M M d p q Edowme regur Ece fuco: regur_eo_edowme (,,,K,) E K A A / K M M / / K d / p p K q
41 Tuor of MS Ece ppco Ipu formo: F pu formo o yeow ces. See pr. Oupu resus: Resus re uomcy ccued gree pr 2. ffere wys of ccuo: See pr 3, dffere pproches o ob sme resu bsed o pu formo. eed ppco of formus: ffere pproches from pr 3 re descrbed pr 4 de. 38
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