Avalable ole at www.scecedrect.com Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 Emergg Markets Queres Face ad Busess The premum for madatory house surace Romaa cosderatos regardg ts facal solvablty Raluca Meda Atal a, * a rgu-mures,540088, Romaa Abstract The surace premum ca be cosdered a detty report betwee the eeds of the sured ad the surer the momet of the creato of the cotractual bod ad the premum resulted from the cotract. Ths must reflect the degree of polcy coverage; t must measure the facal possbltes of the sured ad satsfy equal measure the ecesstes of the surer. A crtcal stage the costructo of the surace product s represeted by the determato of the surace premum whch balaces the facal edurace of the program ad the prce accessblty of ts prce. The preset paper focuses o the optmum level of the madatory house surace Romaa. Ths s based o the calculato model of the premum a surace pool; a attempt to detfy what way the advatages of the house surace outwegh ts flaws. 202 The Authors. 202 Publshed by by Elsever Elsever Ltd. Ope Ltd. access Selecto uder ad CC BY-NC-ND peer-revew lcese. uder resposblty of the Emergg Selecto ad Markets peer revew Queres uder resposblty Face of ad Emergg Busess Markets local Queres orgazato Face ad Busess local orgazato. Keywords: surace; premum; optmum; surace pool. Itroducto The surace report volves a trasfer of surace rsk from the sured to the surer exchage for paymet of a sum of moey by the sured, called premum. Ths s a modest amout compared to ay damage that may occur, sum whch cotrbutes to the establshg the surace fud Cumas, 2003.I ths report, the sured express ther specfc eeds as a cosumer of surace products, eeds that dffer testy from oe dvdual to aother. If these eeds are satsfed, we ca assume that creases customer satsfacto. * The eed * Correspodg author E-mal address: raluca.atal@ea.upm.ro 222-676 202 The Authors. Publshed by Elsever Ltd. Ope access uder CC BY-NC-ND lcese. Selecto ad peer revew uder resposblty of Emergg Markets Queres Face ad Busess local orgazato. do:0.06/s222-567(2)00237-7
830 Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 for a report of detty betwee the eeds of the dscussos betwee the sured ad surer ad the premum resultg from that agreemet should ot be gored. Thus the surace premum should reflect the polcy coverage, to be wth the facal possbltes of the sured, to meet polcyholder ad the surer eeds equally. Regardg the surace premum calculato, academc lterature there are studes amed at determg the optmal sze of ts compoets Asmusse S., 2000; ad Albrecher H., Boxma O., 2004. Of the varous ways to optmze surace premum, partcular the rsk premum, we focused our atteto o the calculato of mmum premum, wth the form of surace called surace pool, tryg to detfy to what extet ths method s applcable to the Romaa system of compulsory surace of homes agast atural dsasters. Isurace premum amout pad by the sured of the surer for the latter to take the rsk of the sured requres cosderato of may elemets, such as rsk premum Albrecher ad Teugels, 2006, proft marg Buhlma H.,984, cost the surer. The surace premum must rse to a amout cosdered suffcet to pay ay damages that may arse durg the cotract of surace to cover expeses for ths perod ad get a reasoable proft for the surer. O the oe had the eed to cover rsks wth ukow frequecy ad testy, ad o the other had because of the exstece of rsks that ca cause great damage, several surace compaes, by mutual agreemet, have created a surace pool whch all ther members collect a pool all premums related rsk groups take uder such coverage. Profts, losses ad expeses are shared amog pool members proporto to premums. Cosderg a pool of surers actg as a sgle surer wth the expoetal premum prcple of rsk ad the we ca detfy a mmum total premum that would crease customer satsfacto, leadg ths way to mprove the supply of surace. I other words, we focus atteto o the optmal szg of the surace premum as a meas of mprovg the supply of surace, because, our opo, the potetal sured use surace oly f the surace premum they must pay s suffcetly reduced compared wth the amout of damage that would cur f the sured evet mght occur. 2. Isurace premum from the perspectve of surace pools 2.2. Isurace pool from geeral to partcular PAID Romaa Poolg volves groupg a large umber of exposure uts so that the law of large umbers mght provde a very accurate predcto of future losses. Ideally t would be a large umber of smlar but ot detcal exposure uts faced wth the same rsks. Thus, poolg volves the dvso of losses betwee group members ad predcto of future losses wth some precso based o the law of large umbers Badea G.D., 2003. The objectves whch we thk were cosdered whe such forms of surace were establshed Romaa mght be: rsk coverage at a reasoable prce for mddle-come people, reduce govermet spedg o coverage geerated by loses caused by atural dsasters ad mprovg rsk culture ad rased awareess about home surace. The system s maaged by a Pool Isurace agast Natural Dsasters Pool de Asgurare împotrva Dezastrelor Naturale, PAID surace - resurace compay formed by surace compaes authorzed to provde compulsory surace for housg accordace wth the law Law o. 32/2000, Law o. 3/990. Operato of such a system requres a partershp betwee publc ad prvate sector as ca be see from Table.
Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 83 Table.Orgasato Structure PAID Admstratve Coucl Status Stucture Allocato of rsk Advsory body Isurace Fud Maagemet Dstrbuto Survellace Support from facal sttutos PAID prvate/publc prvate prvate prvate publc prvate prvate prvate publc NO I Romaa the project was outled through the collaborato betwee the surace market survellace body ad represetatves of surace compaes operatg ths evromet. Dstrbuto s esured both cases through surace compaes. The Romaa system of the 3 compaes whch are part of the surace pool, have dual roles: addto to dstrbuto, through ther represetatves they esure the maagemet of the project. Isurace compaes that dstrbute compulsory housg surace are requred to submt certa formato about the sured, to collect ad sed back the et premums, the surace fud beg thus costtuted, wthout the amout of commsso that they are ettled to, a certa tme frame. Ther commsso was set at 0% of total premums collected. A pre-dsaster rsk maagemet s ofte mssg dsaster-proe coutres, so we cosder t approprate for Romaa to collaborate wth orgazatos that have experece maagg such systems, bodes to support PAID. Damages case the sured rsk occurs must be pad by the surace pool. I a market cotuous chage, cosderg the coveeces of ecoomc crss, ca rase may questos: Who covers the damages f the surace compay whch sured me goes bakruptcy?, f so far there have bee cases of opaymet of compesato, what would dfferetate the ew structure?, who s resposble f surace pool breaks apart?, are fuds maaged such a way, as to be suffcet to cover ay damages that may appear? A publc structure offers extra safety to the sured. 2.2. Premum for madatory surace of houses ad defg elemets of ts calculato formula The surace premum calculato s carred out scetfcally, based o statstcal ad actuaral mathematcs, takg to accout the fluece of factors: the type ad ature of rsks sured, the umber, sze, testy ad degree of dsperso of rsk, the sured amout, durato ad terrtory covered. These factors are amog the elemets that characterze the madatory surace of homes agast atural dsasters Romaa. I Romaa the house, subject of ths surace product, meas, housg, socal housg, housg servces, terveto house, housg eed, housg protocol, holday home Law o. 4/996. For compulsory home surace amout s the maxmum fxed amout establshed two categores of buldgs: type A - 0,000, type B - 20,000, dfferetated by the crtero of buldg materals, dsregardg ts establshmet ad other crtera such as total area habtable ad prce per square meter urba or rural locato, etc.. Romaa legslato does ot specfy that such sured sum updates could occur, oly that the possblty of the surace ad the surace amout could be modfed by govermet decso the frst
832 Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 fve years after etry to force of the preset law ad after ths tme by order of Presdet of the Isurace Supervsory Commsso As stated prevously the premum calculato must reflect the testy of the sured rsk may occur. If you would take to accout oly ths factor owers located hgh-rsk areas would pay excessve premums, volato of the prcple of soldarty Csteleca L., 2004. However dfferetato based o premum rates of rsk areas, dfferetato whch was appled before Romaa optoal earthquake surace for houses, makes the premum to be far relato to a rsk that does ot apply the same way to all sured. The premum should be establshed such a way that ts amout could appeal to cosumers from all areas of rsk, so the surer ca mata a acceptable level of busess eve hgh-rsk areas. Rsks take uder compulsory home surace coverage are rsks that are classfed as part of a class of rsk cosdered atural dsasters, but also a class of rsks that have caused damage that requred great efforts from the state to be covered. It s ths respect, affordablty for relevg the publc authorty, have bee cluded as a compulsory housg surace: earthquakes, floods ad ladsldes PAID Law o.260/2002. Gve the fact that the case of the Isurace Polcy for Dsasters PAD, the rsks covered are earthquakes, floods ad ladsldes, we must dfferetate betwee the costs of the premum for earthquake rsk for whch volutary housg surace s avalable ad the rsk of floodg ad ladsldes. Takg to accout the formato provded by Table 2, we cosder that Romaa s ot amog the coutres whch mortalty rsk for floodg s cocetrated. However, f we cosder the dcators that shape the rsk profle of coutres, we fd that the rsk of floodg Romaa s o average the same rsk class, class four, whch mples a lower average rsk of mortalty due to flood acto. Table 2. The absolute rsk, relatve rsk, ad rsk of mortalty based o rsk classes Romaa Rsks Floods Ladsldes Earthquakes Absolute 4 2 8 rsk Relatve 4 4 7 Rsk Mortalty 4 2 8 Rsk (Source: www.prevetoweb.et) I Romaa rsks assumed, especally earthquakes, recorded a dex level of evrometal rsk ad therefore have bee cluded uder the surace. We cosder a challege for Romaa, takg the three rsks, whch our opo are ot all as strget as the floods have ht our coutry repeatedly over the past years. 3The detfcato of a mmum premum the surace pool 3.. Hstorcal formato about the rsks cluded uder the madatory housg surace Romaa Compulsory home surace s tryg to provde cover for rsks that are costatly threateg the coutry, called the sured rsk, for a oe-year perod, applyg to all property owers be they physcal or legal persos. I Romaa, o the bass of a probablstc rsk study, t was foud that of the eght mllo homes oly te thousad homes may be at rsk ad eed to be compesated, that s oe out of 000 wll have the msfortue to be affected by the sured rsk. So eght mllo people pay compulsory surace premum ad oly 0.% receve compesato, the lablty assumed by the surace pool s realstc.
Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 833 A problem we faced was the lack of data from two perspectves: ether o publc formato o dsasters our coutry s dsclosed to the publc or they do ot exst sytheszed form formato wth respect to floods ad ladsldes Ether the rsk aalyss has ot recorded a great umber of damages pad, aga lmtg our research e.g. earthquake. Earthquakes recorded our coutry betwee 70 ad 2009, have low testes; few are those that exceed a threshold of safety as that of 7 degrees. A earthquake s cosdered a catastrophc earthquake that exceeds the testy 7 o the Rchter scale Specalsts, says that earthquakes Romaa are ot regular, the most recet large earthquakes have occurred Romaa was the years 738, 802, 838, 940 ad 977. Before 850, because there was o urba agglomeratos damage of hgh testy earthquakes were very small, almost oexstet. O earthquake damage 940, states that property damage cocered oly thrty-sx destroyed houses. More accurate formato comes from the 977 earthquake, wth a testy of 7.2 degrees, whch resulted 570 deaths of whch 39 the captal, 7,596 jured, ad damage reached the colossal sum of,400,000,000 U.S. dollars. Accordg to dustry research, a earthquake lke that of 977, could take place betwee 2040 ad 2060. Romaa s grouped to several areas of rsk, dager areas most affected by the earthquake, as part of Moldova ad the Romaa Pla. Sce the scope of the rsk s relatvely small ad the cdece s low, we do ot cosder that t was ecessary to clude ths rsk the compulsory surace. Wth regard to ladsldes, as we have see coutry rsk aalyss, they fall to the category of rsks whose cosequeces are dsastrous, geerally beg assocated wth floods. I the data aalyss we have bult, damage due to ladsldes are cluded the damage caused by floods. Therefore the frst calculato we cosder floods ad ladsldes as oe rsk. Regardg floods, o sgfcat data was obtaed, because oly data o the amout of damages made as a result of floods, are as mea aual value per coutry for a perod of e years was avalable, as show Table 3. Table 3. The damage caused by floods betwee 99 ad 2005 Years 99 997 998 999 2000 200 2002 2003 2005 Damages (0 6 $) 50 0 50 50 00 20 200 33 800 (Source: www.prevetoweb.et) I a frst step we tred to detfy the law of probablty as followed by flood damage. As ca be see the chart below, we foud that flood damage follows a expoetal law. Expoetal law of parameter s used to adjust the amout of damage dstrbuto. To see f flood damage follows a expoetal law usg Cramer vo Mses test the ull hypothess whch assumes that the data follows a expoetal law, whle the alteratve hypothess proposes that the data s ot a expoetal law. Cramer vo Mses test s a crtero used to demostrate the probablty dstrbuto F* compared wth the emprcal dstrbuto fucto gve, t beg a alteratve Kolmogorov-Smrov test. Accordg to Cramer vo Mses Test, wth a probablty greater tha 95%, the ull hypothess s ot rejected ad thus the data follows a expoetal dstrbuto. Oce havg selected the famly laws of probablty that the damage value used to adjust the umber of damages s ecessary to estmate the parameters that defe the law, based o a sample of observatos. To obta pot estmates of parameters of statstcal dstrbutos we use specfc statstcal methods such as maxmum lkelhood method, the method of the smallest squares or the method of momets. Maxmum lkelhood method s usually preferred, because t provdes cosstet ad effcet estmators uder qute geeral whe the sample sze s large eough Mhoc ad Fatu, 2003; coeffcet assocated to the expoetal law s statstcally sgfcat, as
834 Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 the ull hypothess that the coeffcet s 0, s rejected (probablty less tha 0.05). Value of the expoetal law coeffcet s 0.0000056, the amout of whch wll be used calculatg the surace premum. Fg.. The dstrbuto of damages from floods betwee 99 ad 2005 (blue le damages) 3.2. Calculus model of the mmum premum through cosurace We cosder as the sured whch dvdually have expoetal utlty fuctos are wth parameter,, who wat to esure a rsk by defg S radom varables S, S,, S through: 2, S S S2 S () Wth S otg the rsk sured cofrots; S may be, for example, a ew rsk they wsh to take together or may be a stuato where surers have combed portfolos of surace they wat to redstrbute. I our case, the rsk whch we focused was just the flood, the reasos that we have motvated above. Dstrbuto of damage caused by ths rsk s a expoetal law of parameter whose detfed value was 0.0000056. I Romaa, the pool of surace agast dsaster, so oe ca ote the prevous chapter, cossts of thrtee surace compaes. We sought to detfy whether the captal the perod 200-2009, follows a expoetal law utlty parameter,, 3. For ths we used Cramer vo Mses test the ull hypothess whch assumes that the data follows a expoetal law, whle the alteratve hypothess assumes that the data does ot follow a expoetal law. Uder ths test, where a probablty greater tha 95%, the ull hypothess s ot rejected, so the data follows a expoetal dstrbuto. We foud that compoets of the thrtee compaes surace pool, oly for four of them, ABC Isurace SA, Ardaf SA, Geeral Isurace SA, Grawe Isurace SA, the captal follows a expoetal law of. Of those, oly four wll rema uder our study, ABC surace, Ardaf, Grawe Isurace SA, Geeral, as ca be see Table 4. Table 4 Isurace Compaes Ardaf SA SA SA SA 0,000000072 0,0000000065 0,000000054 0,000000048
Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 835 The total premum they eed s: P log E e S (2) The total premum depeds o the choce of S. How should surers to share rsk ad to make the most compettve pool, so to mmze the total premum P? It seems the best choce for surace s whe each of them provdes a fxed part of S, amely: S S, wth (3) I Romaa, partcpato PAID s dfferetated (see Fg..), so three compaes have a share of 5%, whle the remag compoets of the pool compaes have a share of 5%. Oly oe of the compaes uder study s amog those wth major partcpato, amely Ardaf. Gve the route of our demostrato, we assume further that the structure of our pool s lmted to a total of four compaes, wth equal partcpato ad 25%. So = 3856503 + 52000000+ 20599069 + 8429088 = 9204660 RON. Each of surers covers a fracto of the rsk whch s proportoal to the recprocal of rsk averso so the frst correspodg mmum total s: P loge e S log E e S (4) Ths shows that the pool of surers act as oe surer wth a prcple of premum expoetal wth rsk averso. P loge e S log E e S = 257769320 * log(0,0000056/0,0000056-0,0000000038) = 54404660 * log(0,0000056/0,0000055) = 9204660 * 0, 002597 = 496.559 RON Accordg to calculatos, the premum total mmum coverage agast flood rsk s 496,559 RON. Ths value represets the level of the rsk premum, whch wll be loaded wth the value of proft marg expected by the compay ad admstratve costs. After detfyg the gross premum for each buldg separately, t should be dfferetated accordg to dfferet crtera, amely: rsk areas, the types of materals used ad age of buldgs. Sce the surace premum should reflect the degree of polcy coverage, should measure up to the facal possbltes of the sured ad also satsfy the eeds of the surer, t s ecessary to have a relato of detty betwee the eeds of the sured ad surer at the momet the cotract s sged ad the premum resultg from that cotract must ot be eglected,.e. we must detfy the optmal level. The preset aalyss wll be mproved, sce we cosder that the database that was avalable, the structure requred ad the maer of determed the premum surace s ot fully establshed.
836 Raluca Meda Atal / Proceda Ecoomcs ad Face 3 ( 202 ) 829 836 Refereces Cumas, C., 2003. Edtor.. Asmusse, S., 2000. Ru Probabltes,Edtor. World Scetfc, Sgapore. Albrecher, H., Boxma, O., 2004. A ru model wth depedece betwee clam szes ad clam tervals, Isurace Mathematcs ad Ecoomcs, vol. 35 (2), 245 254. Albrecher, H., Teugels, J., 2004. Expoetal behavor the presece of depedece rsk theory, EURANDOM Research Report, vol. 2004 0, TU Edhove Modelg ad Smulato. Gordo & Breach, Newark, pp. 77 96. Buhlma, H., 984.ASTIN Bullet 4, o. 3. Badea, G.D., 2003. Isurace ad resurace, Edtor. Ecoomca, p. 34.