Aals of the Uiversity of Petroşai, Ecoomics, 2(2), 22, 7-76 7 ACTUARIAL TECHNIQUE TO AE THE FINANCIAL PERFORMANCE. INURANCE APPLICATION MIHAELA BOTEA, MARINEL NEELUŢ, CORINA IOANĂŞ, MIHAELA GRUIECU * ABTRACT: The XXI cetury was marked by the covergece ad harmoizatio, this cetury is distiguished i that it lays the foudatio of accoutig actuarial, which is characterized by up to date values ad actuarial calculatios. Actuarial accoutig is reflected best i isurace system. I the market ecoomy, isurace system is o oe had a meas of protectig the busiess ad property of citizes, o the other had a busiess that geerates profits. From this cotet, we ca say that the subject of actuarial accoutig is the measuremet ad recogitio of assets ad result of the chage i time value of moey. Time is a importat variable cosidered i ay ecoomic decisio ivestig ad fiacig. KEY WOR: preset value; actuarial calculatios; assessmet; isurace; maimizig eterprise value; fruitig factor. JEL CLAIFICATION: C; G22; M4.. INTROUCTION Up to date value or capitalized is a estimate at the preset time of the value based o future beefit flows that occur i the ormal course of busiess, meaig updatig a value that becomes available later. Geeral appeal to the IAB, the up to date value is defied i terms of future cash flows at the preset time, the basic priciple adopted is "a pey eared today is worth more tha a pey eared i the future." * Assoc. Prof., Ph.., Academy of Ecoomic tudies, Romaia, mihaela.botea@yahoo.fr Assoc. Prof., Ph.., Fiacial Bakig Uiversity Bucharest, Romaia, edelut@yahoo.com Prof., Ph.., Academy of Ecoomic tudies Bucharest, Romaia, coria_ioaas@yahoo.com Assoc. Prof., Ph.., Romaia America Uiversity, Romaia, mgruiescu@yahoo.com
72 Botea, M.; Nedeluţ, M.; Ioaăş, C.; Gruiescu, M. I this regard, the compay as a idepedet elemet of the ecoomic system iteracts with busiess parters, with budgets from differet levels, capital holders ad other subjects, a process that makes possible the emergece of fiacial relatios. I these circumstaces, the role of accoutig is to provide objective ad accurate iformatio to all users, especially busiess owers ad capital ivestors. The actuarial accoutig: measure ad record possible variatios of iterest rates ad iflatio; quatify i moetary terms the risk of ecoomic activity; estimatio usig actuarial calculatio, measuremet ad recogitio of assets ad profitability usig actuarial calculatio to maimize eterprise value The cocepts of up to date value, preset value ad future value, isurace premiums, auity factor of fructificatio, mortality tables, switchig umbers, techical reserves, mathematical reserves, solvecy, solvecy margi, the isured risk, risk maagemet, actuarial calculatios, accoutig hedgig, time periods, immediate/deferred paymets-collectios, aticipated/ordiary auity paymetscollectios from accoutig of commitmets to the accoutig for treasury, the capital adequacy rules, all forms the actuarial accoutig cotet. To these are added the followig structure: assets as strategic ivestmets, workig capital eeds as fuctioal ivestmet, treasury ivestmet that equilibrium equity fiacig ad equity fiacig raised. 2. ACTUARIAL ACCOUNTING MOEL FOR ETIMATING, RECOGNIZING AN AEING LIFE INURANCE PREMIUM I life isurace the isurer's cocer is to esure the stability of the fiacial results of their activity. He must work i order to fully cover o accout of premiums received, the obligatios assumed to policyholders. Premiums must cover the costs of cotractig, purchasig isurace premiums collected, ad so forth. For this reaso the techique of settig isurace premiums ad mathematical reserve is particularly importat. The calculatio of life isurace premiums is the loss distributio priciple of a perso who has suffered as a result of isurace where, amog may policyholders who have ot suffered ay damage. If paymets are made from the fud arose format all isured as a result of paymet of the isurace premium. The amout of the isurace premium is the epected value of isurace paymets accruig to a isured perso for the duratio of the isurace. Isurace paymets i the form of sum isured, the isurace compay back ad are made if life isurace as a result of death of the isured durig the period of isurace or its survival util the epiry of that period. Thus, to calculate isurace premiums eed to be kow: umber of deaths, the umber of survivors ad the preset value of the amout to be paid i the future (the amout required to be collected by the isurer from the isured to cover future paymets death or survival to a certai age, provided that the proceeds are ivested, for eample capitalized). It follows that, i determiig isurace premiums, start to
Actuarial Techiques to Assess the Fiacial Performace... 73 fructificatio data obtaied from isurace fuds ad the data i the tables of mortality i the coutry aalyzed. 3. FRUCTIFICATION INURANCE FUN To satisfy its obligatios to policyholders, the isured sum paymet o death or o epiry of isurace (survival) isurer creates the accout premiums received from policyholders, a fud, capitalized as bak deposit i circuit ecoomic or other ivestmets, produce icome. Of isurace proceeds by leveragig these fuds are take ito accout i calculatig isurace premium size ad deped o the amout of premiums paid ito the fud, the retetio time i the ecoomic cycle ad fruitig factor. 3. etermiatio of fial value usig the eploit techique A sum of moey paid to fruitio over a period of years, at the ed of that period is: i () - the amout obtaied after fructificatio; - Amout deposited to fruitio; i - Factor of fructificatio; - the umber of years the amout is deposited to fruitio. Eample: A perso aged 25 years isure that is to receive over years, if alive, the amout of 5, lei. The iterest rate is %. To esure survival with maturity over years sigle et premium is as follows: 35 3.3,7569 Pu 5. 5. 5. 66 lei (2) 8.777,6263 25 If appropriate premium amout would be deposited i the bak for the same rate of iterest ad the same time, the at maturity would get the followig amout:, 4. lei F 5. 66 68 (3) Amout obtaied from capitalizig bak deposit is less tha that obtaied from purchase to esure survival. As a result, that perso is more advatageous to coclude esurig survival. 3.2 etermiatio of preset value techique usig update I isurace the iterest is to determie the preset value of amouts to be paid or received over a umber of years. I other words, we ca calculate the amout to be
74 Botea, M.; Nedeluţ, M.; Ioaăş, C.; Gruiescu, M. deposited to fruitio ow, at a certai iterest rate, so that over a umber of years to reach the level epected. The preset value is calculated by updatig techique as follows: (4) v is the discout factor so the formula to update the moetary uit is: i v (5) v - represets the preset value of lio will pay or receive over years, uder a iterest rate i iscout factor idicates how much must be ivested with a effective iterest rate i ad over a year to get the leu. Eample: A isurace compay wats to have the amout of, lei over five years, by depositig a amout X to a credit istitutio where the iterest rate offered is 5%. For this it is ecessary to determie the preset value of the amout of, lei (lei): (6). 784 lei 5 5 % Therefore, the compay must submit to fruitio today the amout of 784 lei with iterest at 5% over 5 years to have the amout of, lei. 4. MORTALITY TABLE AN WITCHING NUMBER Mortality tables iclude a umber of demographic idicators determied based o the umber of survivors ad deaths, by year of birth ad age for me, wome ad both sees ca also be prepared o demographic regio or socio-professioal categories. For some eeds, startig either from geeral mortality tables (complete) or usig estimatio fuctios are costructed abbreviated tables, meas tables for differet itervals betwee ages (for eample from 5 to 5 years). To facilitate the study ad use of the mortality table to calculate isurace premiums, actuarial sciece Actuarial use a Iteratioal ystem of ymbols. Isurace premium calculatio i life isurace requires demographic idicators of mortality table ad data update factor values obtaied from fiacial tables updated. I practice it is desirable to estimate the actuarial premium rates for each age ad duratio of isurace accepted by the isurer, which cotributes to the eormous performace of arithmetic operatios based o large data sets. To simplify calculatios premium rates, life isurace techique uses a umber of auiliary quatities called switchig values that are part umbers switchig table. These values are obtaied by combiig idicators icluded i the fiacial tables of
Actuarial Techiques to Assess the Fiacial Performace... 75 mortality tables ad updatig. Thus, substitutio occurs (switchig) figures i these two tables with differet values ad their aggregatio ito a sigle table. Calculatios predetermied switchig table umbers, takig ito accout the sum isured base equal to oe. Table. witchig values obtaied with the umber of survivors l Formula Eplaatio of the formula l v Preset value of the product of the umber of survivors to age ad sum isured uit. Preset value of the product N... t of the umber of survivors t ad the sum isured uit. Table 2. witchig values obtaied with the umber of deaths d Formula C d v M C C... C t C t Eplaatio of the formula Up to date value of the product of the umber of deaths by age ad sum isured uit. Up to date value of the product of the umber of deaths ad the sum isured uit. 5. CAE TUY ON AEMENT, RECOGNITION AN MEAUREMENT OF PREMIUM LIFE INURANCE A perso uder the age of 3 years makes a life isurace, the isurace compay "AVIVA" A by isurace aget, which is to receive the ed of each year the amout of 2. lei lifetime. Isurace aget cotract betwee the isurace compay ad aget commissio set was % of premiums eared. I these coditios: First sigle et is as follows: P N N 3 5.48,876 Pu a 3 2 2. 8. 663 lei 5.43,27964 (7) 3 Accordig to legal provisios, the isurace aget commissio due, the compay calculated, withheld ad remitted state budget a % advace ta accoutig (8,663 % = 866.3 lei). 6. CONCLUION Uderlyig problem that appears i the literature i Romaia is caused by the fact that at preset there is o up to date accoutig, customized for system evaluatio, recogitio ad calculatio. Therefore, the value of the work is to develop a ew
76 Botea, M.; Nedeluţ, M.; Ioaăş, C.; Gruiescu, M. cocept - the actuarial accoutig - that would help improve the methodological basis of accoutig isurace compaies i Romaia, which will: iclusio i icome of isurace compaies oly portios of the first obtaied from direct isurace ad reisurace wo so will eclude cases of distortio of iformatio i the fiacial statemets set for those operators; better estimatio of isurace risk, which makes the iformatio preseted i the fiacial statemets is closer to the priciple of true ad fair view; stability of the fiacial results of activity due to the full coverage premiums received o accout of obligatios to policyholders ad costs related to sigig cotracts ad premiums collected; fructificatio ad updatig techiques i determiig the fial value ad the actual value; take ito accout i determiig isurace premiums i the umber of deaths, umber of survivors, the curret value of the amout to be paid i the future (the amout required to be collected by the isurer from the isured to cover future paymets o death or survival to a certai age, provided that the proceeds are ivested, for eample capitalized); use mortality tables ad umbers switchig to a better estimate of premiums; use the method "pro rata" i calculatig ueared premium reserve at the ed of the reportig period by isurace orgaizatios i Romaia. Usig this method raises the level of accuracy of calculatio of actual icome eared from isurace busiess durig the reportig period, ecludig cases where the isurer, i the period of the isurace cotract, has o meas the ueared premium reserve ad guaratee the performace by it the obligatios assumed uder the coditios stipulated i isurace REFERENCE: []. Epstei, B.J.; Mirza, A. (25) IFR 25 Iterpretarea şi aplicarea tadardelor Iteraţioale de Cotabilitate şi Raportare Fiaciară, Bucureşti, BMT [2]. Ceuşă, G.; Burlacu, V. (2) Bazele matematice ale asigurărilor, Ed. Teora, Bucureşti [3]. Ciurel, V. (2) Asigurari si reasigurari: abordari teoretice si practici iteratioale, Ed. All Back, Bucureşti [4]. ayki, C.. (992) The evelopig Role of the Govermet Actuary s epartmet i the upervisio of Isurace, Joural of the Istitute of Actuaries, vol. 9, part II, o. 473 [5]. ayki, C..; Petikaie, T.; Pesoe, M. (993) Practical Risk Theory for Actuaries, Chapma&Hall [6]. obri, M. (25) Cotabilitatea specifică domeiului asigurărilor, Ed. Bre, Bucureşti [7]. Gart, A.; Nye,.J.; Harriso, C.M.; Gibbos, R.J. (994) Isurace Compay Fiace ad Ivestmets, Isurace Istitute of America, Malver, Pesylvaia [8]. Murray, A.; Gohil, H.; Buckley, K.; Burke, J. (24) Mid the GAAP: Fitch s view o Issurece IFR pecial report Fitch Ratigs [9]. http://www.cea.assur.org []. http://www.actuaries.org []. http://www.jia.com [2]. http://www.iasb.com