Forecasting general insurance loss reserves in Egypt

Transcription

1 African Journal of Business Managemen Vol. 5(22), pp , 30 Sepember, 2011 Available online a hp:// DOI: /AJBM ISSN Academic Journals Full Lengh Research Paper Forecasing general insurance loss reserves in Egyp Tarek Abd Elhamid Ahmed Taha 1, Yusnidah Ibrahim 2 * and Mohd Sobri Minai 2 1 College of Commerce, Tana Universiy, Egyp. 2 College of Business, Universii Uara Malaysia, Malaysia. Acceped 1 June, 2011 Loss reserve is one of he mos imporan indicaors ha have many imporan and sraegic decisions applicaions, such as rae making decisions, underwriing decisions, invesmen decision and corporae planning. The aim of his sudy is o idenify he reliable ime series forecasing model o forecas loss reserve esimaes of Egypian general insurance companies. Exponenial smoohing model, Box-Jenkins analysis and ime series regression model are applied on acual repored loss reserves daa for general insurance secor for he period 1986 o 2006 and heir accuracy are compared based on several error measures. The series from 1986 o 2001 are used for he esimaions process and he remaining observaions are used o evaluae he models as ouside sample daa. Exponenial smoohing echnique in all seps-ahead is idenified as he bes forecasing echnique o Egypian general insurance secor. Key words: General insurance, echnical reserve esimaion, ime series forecasing. INTRODUCTION One of he major asks ha insurance companies rouinely perform is loss reserves esimaion. Loss reserves, also referred o as claim reserves, are esimaes of wha claims will cos. The reserve represens money ha is se aside o mee claims arising in he fuure on he policies already wrien (England and Verrall, 2002). In oher words, he claim reserving process is a prospecive esimaion of wha claims will cos o he insurance company. The principal aim of reserving esimaion is o insure he proecion of policyholders (Cheung, 1997). Apar from ha, loss reserving has imporan implicaions for insurers pricing and compeiive responses. If he esimae of loss reserves were oo low, premiums would be inadequae o suppor he financial projecions of fuure periods. In he wors case scenario, rae would be insufficien o pay claims and he company would be insolven, if he loss esimaes were oo high, consequenly, insurance raes may be raised above compeiive levels (Douglas, 1999; Calandro and O'Brien, 2004). Furhermore, general insurers need o be able o esimae loss reserves o make sure ha hey have sufficien asses o cover heir liabiliies. Insolven insurance companies are *Corresponding auhor. yibrahim@uum.edu.my. Fax: no allowed o coninue o sell insurance policies because i does no have he financial srengh o keep is conracual obligaions o is policyholders (Cheung, 1997). Loss reserves esimaion are also imporan for ousiders in deermining he financial liabiliy, financial srengh and value of an insurance company (Cheung, 1997). Loss reserves are collecively he larges liabiliy on a propery and liabiliy insurer s balance shee, hus any under-reserving of losses will decrease an insurer s liabiliies and boos is ne income (Grace and Lavery, 2006). Loss reserves in general insurance marke are esimaed based on acuarial reserving echniques such chain ladder echnique (CLT) (Harnek, 1966), Bornhueer Ferguson echnique (BFT) (Bornhueer and Ferguson, 1972) and Taylor separaion echnique (TST) (Taylor, 1977). Neverheless, daa required by all hese reserve esimaion echniques is complex and ambiguous, where i is assumed ha he claims paid can be grouped according o acciden years and developmen years, resuling a claim run-off riangle (Panning, 2006). Considering he imporance of loss reserve figures for fuure planning and decision-making and he complexiy and ambiguiy of acuarial loss reserve calculaion, i is beneficial o explore non-acuarial approaches o esimaing loss reserves; one of hem is he ime series forecasing echnique. Hence, his sudy aims is o

2 8962 Afr. J. Bus. Manage. compare he accuracy of several ime series forecasing echniques, namely exponenial smoohing model, Box- Jenkins analysis and ime series regression model, in order o idenify he bes forecasing model. To he auhors knowledge, here are only a few sudies ha explore he uilizaion of ime series forecasing model in reserves esimaion. PRIOR RELATED STUDIES Sudies ha uilize ime series echnique o forecas loss reserve is scarce. Harbey (1995) used muliple regression echnique o esimae he ousanding loss reserve in Egypian general insurance marke wihin he period from 1980 o He found ha ousanding claim reserve esimaion is affeced by wo variables, namely, underwriing premiums and paid claims, Harbey (1995) reached he possibiliy of applying he muliple regression models o some general insurance segmens and could no be applied o ohers. Doray (1996) considered he problem of forecasing he number of claims incurred. Afer subracing he number of claims repored o dae, he number of claims incurred bu no repored (IBNR), which is he main porion of loss reserves, can be forecas. The basic model assumes ha he number of claims per acciden period follows an auoregressive moving average ime series process. Insead of assuming he daa available in he usual claim run-off riangle forma, he assumed ha he only daa available are he number of claims repored a he valueion dae for each acciden inerval of an observaion period. Box-Jenkins mehods are used o forecas he ulimae number of claims incurred and o obain approximae confidence inervals for he number of claims incurred. Chan e al. (2004) used he growing riangle echnique (GT) for comparing beween differen models for loss reserve esimaion including CLT which based on weighed average mean square error, CLT based on simple average mean, Bornhueer- Ferguson, and lognormal model. A he base of GT echnique, sub-riangle of losses, embedded in he full riangle of available daa, are used o evaluae he predicion power of various candidae mehods of esimaion. The GT echnique is illusraed using hree daa ses: i) paid losses during 1978 o 1995 ii) paymens per claim during 1981 o 1995 iii) number of claims noified during 1985 o Based on weighed mean square error (WMSE) for he hree run-off riangle, Chan e al. (2004) found ha CLT based on he simple average provides he bes predicion for he second and he hird daa ses. Also, Chan e al. (2004) found ha he CLT echnique produces relaive consan resuls in he growing riangle assessmen, his is explained by he relaive simple and non-parameric naure. On he oher hand, he found ha he log-normal model is he bes model for he firs daa se. Bai e al. (2005) esimaed loss reserves in he US denal insurance based on radiional model which is he CLT and suggesed wo models namely log-linear regression model and ime series model based on he holwiner seasonal algorihm. Using daa from General Moors employees provided by Dela Denal and using he CLT mehod on General Moors daa from January 2001 o December 2002, hey found ha he radiional CLT model is viewed as being inadequae in he ligh of he error raes which are calculaed based on he difference beween oal esimaed reserve and he acual oal reserve. Using he log-linear regression model on daa from various corporae plans, and comparing he esimaed values wih he acual loss reserves, he resuls show ha he variaion in he error raes are very high and i is difficul o ell in advance if he predicion is going o be accurae. They also found ha he model based on ime series analysis using he Hol-Winers seasonal algorihm which is designed o handle boh rend and seasonal variaion in he daa is performed well on many daa ses by decreasing he error raes. They found ha many echniques did no esimae denal insurance reserve wih consan accuracy, some of suggesed echniques performed well for cerain daa ses and performed poorly on ohers. They noiced ha some of hese models such as CLT and ime series required 24 o 36 monhs of hisorical daa while log-linear regression model required only 13 monhs daa. So, for new insurer s, modeling wih ime series may no be possible. They concluded ha here seems o be no model ha will be boh accurae and consan for all daa ses. RESEARCH METHODOLOGY Forecasing models Three ime series mehods are used o esimae loss reserves. These model forecass are compared o he acual values of he daa, and he forecasing models are ranked and compared depending on heir sandard error. Exponenial smoohing echnique This echnique is a mos widely used class of univariae ime series modeling echnique and is a very popular scheme o produce a smoohed ime series (Lazim, 2005). Whereas in moving averages, he pas observaions are weighed equally, exponenial smoohing assigns exponenially decreasing weighs as he observaion ges older. In oher words, recen observaions are given relaively more weigh in forecasing han he older observaions. In exponenial smoohing models, he forecas for he nex and all subsequen periods are deermined by adjusing he curren period forecas by apporion of he difference beween he curren forecas and he curren acual value. In Brown s mehod, only one smoohing consan is used and as such, he esimaed linear rend values obained are sensiive o random influences. To overcome his problem, he sudy uses he Hol s mehod, which is a echnique frequenly used o handle daa wih linear rend. This mehod does no only smoohen he rend and he slope direcly by using differen smoohing consans, bu also provides more flexibiliy in selecing he raes a which he rend and slopes are racked. The applicaion of Hol s mehod requires hree equaions: he

3 Taha e al exponenially smoohed series: s y (1 )( s 1 T 1) : T The rend esimae, he rend esimae is calculaed by aking 1 he difference beween wo successive exponenial smoohed values(s - S -1): T ( s s ) (1 ) 1 1 A second smoohing consan β is used o smooh he rend esimae. In his equaion, he esimae for he rend (S - S -1) is muliplied by he smoohing consan β. This value is hen incorporaed ino he previous esimae of he rend ha has been adjused by he facor (1-β). The smoohing is done for he rend raher han for he acual daa, his resul in a smoohed rend wihou any randomness: F m s T m The values of α and β are he parameers o be deermined wih values ranging from 0 o 1. BOX-Jenkins model (ARIMA) The ARIMA sands for he combinaion ha comprises of auoregressive/inegraed/moving average models. I is commonly applied o ime series analysis, forecasing and conrol. The basis of he Box-Jenkins / (ARIMA) modeling approach consiss of hree main sages: model idenificaion; model esimaion and validaion; model applicaion. Model idenificaion: The firs sep in he applicaion of he Box- Jenkins mehodology is o idenify he class of model mos suiable o be applied o he given daa se. This is done by compuing, analyzing and ploing various saisics based on hisorical daa. Common saisics used o idenify he model ype is he auocorrelaion funcion (ACF), and he parial auo-correlaion funcion (PACF). Hence, he common pracice now is o idenify several highly likely model formulaions and subsequenly choose he bes model ha mees all saisical requiremens. The process of idenifying he models is, hus, summarized as follows: 1. To compue and analyze he various saisics based on he hisorical daa, in paricular he ACF and he PACF. 2. Based on informaion obained from 1 above, he mos suiable subclass of he general class of model is hen idenified. Model esimaion and validaion: The specific parameer values are esimaed subjec o he condiion ha he seleced error measure is minimized. More specifically, he process is o search for he esimaed parameer values ha minimize he differences beween he acual and he forecas values. series; new model is formulaed and re-esimaed; develop a sysem o monior he forecas values produced. Assumpion of Box-Jenkins mehodology: The applicaion of he Box-Jenkins mehodology lies on he assumpion ha concerns he characerisic of he iniial daa series (Lazim, 2005). Basically, i is assumed ha he daa series is saionary. Where such assumpion is no me, hen he necessary procedures are performed in order o achieve saionary in he series. A simple procedure used o remove he non-saionary in ime series is o perform he differencing, and log ransformaion is commonly used o sabilize he variance. There are four basic models: i. The auoregressive (AR) model, ii. The moving average (MA) model, and iii. Mixed auoregressive and moving average model. iv. Mixed auoregressive, Inegraed and moving average model. i. The auoregressive (AR) model In he AR model, he curren value of he variable is defined as a funcion of is previous values plus an error erm (Lazim, 2005). Mahemaically, i is wrien as: y 1 y 1 2y 2... p y p Where and ( j 1,2,... p ) are consan erms or j parameers o be esimaed, y : is he dependen or curren value and y he p h. order of he lagged dependen or curren value, p and : is he error wih mean=0 and variance 2 e. ii. The moving average model (MA) model The moving average is a funcion of he error erms; he moving average model links he curren values of he ime series o random errors ha have occurred in he previous periods raher han he values of he acual series hemselves. The moving average model can be wrien as: y q q Where is he mean abou which he series flucuae, ' are he s moving average parameers o be esimaed, and q' s are he error erms (q=1, 2, 3,..) assumed o be independenly disribued over he ime. iii. Mixed auoregressive and moving average model Model applicaion: If all es crieria are me and he model s finess has been confirmed, i is hen ready o be used o generae he forecass values. A his sage, hree possibiliies may occur; new or laes daa are colleced and incorporaed ino he exising Under he assumpion of saionary, he mixed auoregressive and moving average model of Box-Jenkins mehodology is known ARMA model. In oher words, he series is assumed saionary (no need for differencing) and he model is wrien as: y y y... y p p q q Since he AR and he MA models are of order p and q respecively, he model is referred o as ARMA (p, q).

4 8964 Afr. J. Bus. Manage. iv. Mixed auoregressive, inegraed and moving average (ARIMA) model When he daa is no saionary, hen he Box-Jenkins (ARIMA) mehodology is represened as ARIMA (p, d, q), where d denoes he degree of differencing involved o achieve saionariy in he series. Time series regression model The ime series regression models relae he variable y o a funcion of ime. Time series y can be described using a rend model; such model is defined as follow: y TR 0 1 Where, y : The value of he ime series in period ; TR : The rend in he ime period ; : The error erm in he ime period. Any one value of he error erm is saisically independen of any oher value of he error. In oher words, serial correlaion problem mus no exis. To correc he serial correlaion problem, Cochrane- Orcu procedure is applied o produce beer esimaes. F-es saisic is used o es he overall finess of he model while -es is used o idenify which variables o be included in he final model. Adjused R-squared is hen used o measure he goodness of fi of he model. Models evaluaion The accuracy of model s performance is measured by he size of he forecas error. The operaional meaning of an error is defined as he difference beween he acual value and he fied value generaed from a given model by e y y. So, he bes mehod will give us he smalles error value. Error measures This sudy uses four measures of error ha are commonly discussed and uilized by researchers and praciioners, namely, mean squared error (MSE), roo mean square error (RMSE), mean absolue percenage error (MAPE) and geomeric roo mean squared error (GRMSE) (Armsrong and Collopy, 1992; Lazim, 2005). Mean squared error (MSE) 2 e MSE n For which e y y where y is he acual observaion and y is he esimaed value. Is srengh lies in is mahemaical simpliciy, ha is, i is easy o undersand and o calculae, i has he endency o penalize large forecas errors more severely han oher common accuracy measures o deermine which mehod avoid large errors. In oher words, an incidence of a large error would significanly influence he value of MSE. Bu he main disadvanage he MSE faces is ha i is easily affeced by exreme values. Roo mean square error (RMSE) This is he mos favored measure among he praciioners and has even sronger preference among he academics. RMSE n e 2 The RMSE gives equal weighs o all errors; his can also be disadvanageous o a model ha has one large forecas error. Thus, when an analys ranks he forecasing models by RMSE, he presence of one or wo exreme errors may aler he ranking of he model. Mean absolue percenage error (MAPE) MAPE n 1 ( e / y) 100 n The main disadvanage of his measure lies in is relevancy as i is valid only for he raio-scaled daa (ha daa wih a meaningful zero). For his reason, MAPE is poenially explosive for large forecas error when he acual observaions are close o zero. Geomeric roo mean squared error (GRMSE) n GRMSE ( e ) n The exisence of an oulier grealy affecs he accuracy of he error measure. Bu he geomeric roo mean square error is he mos useful alernaive in his case. Daa collecion The Egypian marke is he objec of his sudy, and he sudy will concenrae on loss reserves in general insurance segmen wihin he years 1986/1987 ill 2006/2007. Daa encompasses of loss reserve value for he oal general insurance indusry. A oal of 21 annual daa is used. FINDINGS Figure 1 shows a plo of he yearly observaions for loss reserves in he Egypian marke from he year 1986/1987 o he year 2006/2007. This plo exhibis a rend paern because i appears o be an upward rend in he daa. There is also rises and falls in his ime series wihin he period 1995/1996 o 1998/1999 afer ha i coninued o rise seadily unil 2006/2007. Models esimaion Ou of 21 annual observaions of loss reserves in he Egypian marke, 16 observaions will be used o esimae he following forecasing models:

5 1986/ / / / / / / / / / / / / / / / / / / / /2007 Reserves Taha e al Figure 2.Technical Reserves in General Insurance in The Egypian Marke Years Figure 1. Loss reserves in general insurance in he Egypian marke. The verical axis measures he variable loss reserves in he Egypian marke (dependen). The horizonal axis corresponds he ime periods (independen). E.P, 000. Table 1. Fied model based on exponenial smoohing echnique. T Y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep / * / ** * / *** ** * / **** *** ** / ***** **** *** *1 16 observaions used in he esimaion process; **1 17 observaions used in he esimaion process; ***1 18 observaions used in he esimaion process; ****1 19 observaions used in he esimaion process; *****1-20 observaions used in he esimaion process. 1. Exponenial smoohing model 2. Box-Jenkins (ARIMA) model 3. Time series regression model These models forecass will be compared o he acual values of he daa, and he forecasing models will be ranked and compared depending on he sandard error. Exponenial smoohing echnique Based on he Hol mehod, he bes Alpha, Gamma and Dela combinaion are: A = 1.00 alpha, G = 0.00 gamma. The fied model is presened in Table 1. BOX-Jenkins model (ARIMA) Auocorrelaion funcion (ACF) inspecion: As shown in Figure 2, he firs spike of ACF values is large and i declines speedily o zero, herefore, we can conclude ha he series is saionary, and i does no need o do differencing, and he number of significan spikes equal 4, so MA(4) can represen his daa series. Parial auocorrelaion funcion (PACF) inspecion: Figure 3 shows here is significanly large spike followed by smaller oher spikes a lags higher han 1. This means ha he series is saionary wih one significan spike, so, he AR (1) model can represen his daa series. Fiing he ARIMA model: For comparison purposes, 5 models were esimaed, ha is, ARIMA (1, 0, 4), ARIMA (1, 0, 3), ARIMA (1, 0, 2), ARIMA (1, 0, 1), and ARIMA (1, 0, 0). To deermine which of he models fis he bes, wo crieria will be used; he firs crieria is he value of AIC/SBC (Akaike s informaion crieria) and he second, he value of he MSE. The resuls are summarized in Tables 2 and 3. Hence i is concluded ha ARIMA (1, 0, 2) model is relaively he bes model since i has he smalles AIC and SBC. T- ess execued on ARIMA (1,0,2) model indicae ha AR(1) can represen he model a 1%

6 Parial ACF ACF 8966 Afr. J. Bus. Manage. Reserves Coefficien Upper Confidence Limi Lower Confidence Limi Figure 2. Auocorrelaion funcion (ACF) Lag Number Reserves Coefficien Upper Confidence Limi Lower Confidence Limi Lag Number Figure 3. Parial auocorrelaion funcion (PACF). significan level (Table 4). Applying AR (1) forecasing model on he acual loss reserve daa resuled in he esimaed daa ( y ) in Table 4. Time series regression Since he daa series have a rend and does no have seasonaliy (yearly daa), he model ha beer represens he daa is: y = TR + ε. The linear model ha represens y he daa series is herefore 0 1 Normaliy analysis as presened in Table 5 and Figure 4 indicaes ha he disribuion of loss reserve is close o a normal disribuion. Afer correcing for serial correlaion problem using Cochrane-Orcu mehod, he final esimaion model is presened in Table 6. In summary, based on he Table 6, he following

7 Taha e al Table 2. AIC and SBC summary able. Saisic Model form ARIMA (1, 0, 4) ARIMA (1, 0, 3) ARIMA (1, 0, 2) ARIMA (1, 0, 1) ARIMA (1, 0, 0) AIC SBC Table 3. Variables in he model. Variable B SEB T-RATIO P-value AR1* MA MA Consan *represen significan a 1% level. Table 4. Fied model based on BOX-Jenkins model. T y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep 2002/ * / ** * / *** ** * / **** *** ** / ***** **** *** *1 16 observaions used in he esimaion process; **1 17 observaions used in he esimaion process; ***1 18 observaions used in he esimaion process; ****1 19 observaions used in he esimaion process; *****1-20 observaions used in he esimaion process. y represens he acual loss reserve evaluaion values. y represens he forecased value. e is he predicion error, calculaed by aking he differen beween y and y. Table 5. Normaliy hrough SPSS. Variable Saisic Skewness Sd. error z-score (<2) Saisic Kurosis Sd. error z-score (<7) Tes of normaliy Kilmogorov-Smirnov Significance Saisics 0.05 Reserves Normal Z-sa skewness = skewness/sd error skewness= skewness saisics/.501; Z-sa kurosis = kurosis/sd error kurosis = kurosis sais. Descripion of disribuion equaions will be used o predic y-values based on he series lenghs: y 0 1 y y (Series lengh: 19) (Series lengh: 20) y y y (Series lengh: 16) (Series lengh: 17) (Series lengh: 18) Models evaluaion and comparison Each of he forecasing models is evaluaed based on several error measures. The errors are repored in Tables 6 o 10. A comparison is also made across resuls from differen

8 Expeced Cum Prob 8968 Afr. Figure J. Bus. Manage. 5.Normal P-P Plo of Regression Sandardized Residual 1.0 Dependen Variable: Reserves Observed Cum Prob Figure 4. Normal p-p plo regression sandardized residual. Table 6. Time series regression models of loss reserve. Unsandardized coefficiens Sandardized coefficiens Model Sig. β Sd. Error Bea 16 Obs. (Consan) Obs. (Consan) Obs. (Consan) Obs. (Consan) Obs. (Consan) Table 7. Fiing he model. T y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep 2002/ * / ** * / *** ** * / **** *** ** / ***** **** *** *1 16 observaions used in he esimaion process; **1 17 observaions used in he esimaion process; ***1 18 observaions used in he esimaion process; ****1 19 observaions used in he esimaion process; *****1-20 observaions used in he esimaion process.

9 Taha e al Table 8. Exponenial smoohing echnique. T y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep 2002/ / / / / MSE RMSE GRMSE MAPE Table 9. BOX-Jenkins model (ARIMA). T y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep 2002/ / / / / MSE RMSE GRMSE MAPE Table 10. Time series regression. T y y 1- sep y 2- sep y 3- sep e 1- sep e 2- sep e 3- sep 2002/ / / / / MSE RMSE GRMSE MAPE mehods for one-sep ahead; wo-sep ahead and hreesep ahead. This evaluaion o idenify which mehod has a beer predicion. This evaluaion will be presened in he Tables 11a, b and c.

10 8970 Afr. J. Bus. Manage. Table 11a. One-sep-ahead evaluaion. Technique MSE RMSE GRMSE MAPE Toal Exponenial (1) (1) (1) (1) 4 ARIMA (3) (3) (3) (3) 12 TSR (2) (2) (2) (2) 8 Table 11b. Two-sep-ahead evaluaion. Technique MSE RMSE GRMSE MAPE Toal Exponenial (1) (1) (1) (1) 4 ARIMA (3) (3) (3) (3) 12 TSR (2) (2) (2) (2) 8 Table 11c. Three-sep-ahead evaluaion. Technique MSE RMSE GRMSE MAPE Toal Exponenial (1) (1) (1) (1) 4 ARIMA (3) (3) (3) (3) 12 TSR (2) (2) (2) (2) 8 From Table 11a, i is easy o say ha he bes forecasing echnique for 1-sep ahead is he exponenial smoohing echnique. Tables 11b and c shows ha he bes forecasing echnique for 2-sep and 3-sep ahead is also he exponenial smoohing echnique. These comparisons conclude ha exponenial smoohing echnique is he bes ime series forecasing model for general insurance loss reserve in Egyp. Conclusion The aim of his sudy is o apply ime series analysis o forecas he loss reserves in general insurance in he Egypian marke. The forecased loss reserves are one of he mos imporan indicaors ha have many imporan and sraegic decisions applicaions. For all he adoped models, he esimaions are done by using he loss reserves daa in general insurance in he Egypian marke for he period 1986 o The series from 1986 o 2001 were used for he esimaions process and he oher remaining observaions (daa from 2002 ill 2006) are used o evaluae he models as ouside sample daa. The models are evaluaed based on heir accuracy in predicing ouside sample daa. The sudy concludes ha he bes model is he exponenial smoohing echnique in all seps-ahead. REFERENCES Bai Y, Barger C, Olandese A, Singh N, Sunesara R (2005). Esimaing loss reserves for denal claims. Michigan Sae Universiy, from: Brown M (1996). Modeling and forecasing in insurance managemen. A guide o insurance managemen. edied by: Sephen Diacon. Macmillan, pp Bornhueer RL, Ferguson RE (1972). The acuary and IBNR. Proc. Casualy Acuarial Soc., 59: Calandro J, O'Brien T (2004). A user-friendly inroducion o properycasualy claim reserves. Risk Manage. Insur. Rev., 7 (2): Chan JSK, Choy STB, Makov UE (2004). The growing riangle echnique for choosing a mehod of loss reserves. Proceedings of he 3rd Conference in Acuarial Science and Finance, held in Samos. on Sepember 2-5. From: hp:// mainpage.hm Cheung D (1997). Esimaing IBNR Reserves wih Robus saisics. Unpublished Ph.D. Thesis. Wesern Michigan Universiy, U.S.A. Douglas D (1999). Comparaive Analysis of neural neworks and radiional Acuarial mehods for esimaing casualy reserve liabiliy. Unpublished Ph.D. Thesis. The Universiy of Texas, U.S.A. England PD, Verrall RJ (2002). Sochasic claims reserving in general insurance. London: Insiue of Acuaries, pp Grace MF, Lavery JT (2006). Propery-Liabiliy Insurer Reserve Error: Manipulaion, Misake, or Moive. World Risk and Insurance Economics Congress. Harbey G (1995). Using regression model echnique in esimaing ousanding claim reserve in propery and liabiliy insurance. J. Financ. Commercial sud., Faculy of commerce. Beni Sueif. Cairo Univ., 5(1). Harnek RF (1966). Formula loss reserves. Insurance Accouning and saisical Proceedings. Lazim MA (2005). Inroducory Business Forecasing. Shah Alam: Uim. Taylor GC (1977).Separaion of inflaion and oher effecs from he disribuion of non-life insurance claim delays. ASTIN Bull., 9: Armsrong JS, Collopy F (1992). Error measure for generalizing abou forecasing mehods: Empirical comparison. In. J. Forecas., 8: