Ordinal Classification Method for the Evaluation Of Thai Non-life Insurance Companies

Transcription

1 362 Ordil Method for the Evlutio Of Thi No-life Isurce Compies Phiboo Jhopit, Sukree Sithupiyo 2 d Thitivdee Chiywt 3 Techopreeurship d Iovtio Mgemet Progrm Grdute School, Chullogkor Uiversity, Bgkok, Thild 2 Deprtmet of Computer Egieerig, Fculty of Egieerig, Chullogkor Uiversity, Bgkok, Thild 3 Deprtmet of Sttistics, Fculty of Commerce d Accoutcy Chullogkor Uiversity, Bgkok, Thild Abstrct This pper proposes use of ordil clssifier to evlute the ficil solidity of o-life isurce compies s strog, moderte, wek, d isolvecy. This study costructed efficiet clssifictio model tht c be used by regultors to evlute the ficil solidity d to determie the priority of further exmitio s erly wrig system. The proposed model is beeficil to policy-mkers to crete guidelies for the solvecy regultios d roles of the govermet i protectig the public gist isolvecy. Keywords: Ordil clssifictio, Imblced clss clssifictio, Solvecy coditio clssifictio, No-life isurce compies.. Itroductio Thild Isurce idustry is subject to govermet regultio to protect policyholders, third-prty libility climt, d other relted busiess. Solvecy supervisio, regultios d solvecy positio clssifictio is importt topic for o-life isurers. Most of the studies were implemeted i the Uited Sttes d my previous studies focused o biry clssifictio d the problem whose clss vlues were uordered (bkrupt/obkrupt, solvecy/isolvecy, or helthy/filed)[2-6]. Ufortutely, they were ot implemeted i the multiclss clssifictio fshio. I this pper, we hece proposed ordil multi-clss clssifictio for solvecy coditio clssifictio. Normlly, The Office of Isurce Commissio (OIC) of Thild uses the Cpitl rtio (CAR) system of o-life isurce i 2009 to evlute the cpitl dequcy or ficil solidity of the o-life isurers (s show i Tble ). With the coditio distiguished by level of CAR, the isurce compy d regultor s ctios re required. TABLE The solvecy evlutio d regultory ctios bsed o CAR system. Clss Strog Moderte Wek Cpitl dequcy rtio (CAR) 50% 20-50% 00-20% The ctio level No ctio level Compy ctio level Regultory ctio level Isolvecy < 00% Authorized cotrol & Mdtory cotrol level Note: Compy ctio level - compy must file pl with isurce commissioer & expliig cuse of deficiecy d how it will be corrected. Regultory ctio level - The commissioer is required to exmie the isurer d tke corrective ctio, if ecessry. Authorized cotrol level & Mdtory cotrol level - The commissioer hs legl grouds to rehbilitte or liquidte the compy, the commissioer is required to seize compy. The level of cpitl dequcy rtio (CAR) of isurer is ffected by most isurce ctivities d decisio mkig processes such s premium rte mkig, determitio of the techicl reserve, risk udertkig, reisurce ctivities, ivestmet, sles, credibility of compy to relted prty, d lso be ffected by the coutry s ecoomy, ew legisltios, ifltio d iterest rtes []. With the help of our system, the compies c erly detect the solvecy coditio of their ow d c decide the most suitble policy to reduce their risk.

2 Literture review Amog my empiricl studies of isurce sciece, there re severl studies with differet techiques used for improvig the performce of Isolvecy predictio d/or clssifictio model. Most studies pplied trditiol sttistic techiques, such s regressio lysis [2], multivrite discrimit lysis (MDA) [3, 4, 5], logistic regressio (LR) [6], logit d probit model [7-0], d multiomil logistic regressio (MLR) []. O the other hd, mchie lerig techiques such s eurl etworks (NNs) [-5], d geetic lgorithm (GA) [6] were lso used i Isolvecy predictio. Krmer (997) evluted the ficil solidity of Dutch o-life isurce by combiig trditiol sttistic techique (ordered logit model) with rtificil itelligece techiques ( eurl etwork d expert system). The complete model cotis three progrms; logit model, eurl etwork, d expert system. The dt from yer 992 hs bee used s triig dt set d yer 993 s the test set. The output of the multi-clss clssifictio model cosists of the priority for further exmitio (High, Medium, d Low clss). The system which evlutes the ficil solidity c be used to clssify the isurers ccordig to their degree of risk exposures. The model correctly clssified 93% of the dt test set. It showed very good performce for strog, medium d wek compies, 96.3% of the strog, 75.0% of the medium d 94.4% of the wek re clssified correctly. Pitselis (2009) studied the solvecy supervisio, regultios d isolvecy predictio of Greece isurce compies usig sttisticl methodologies, e.g. discrimit lysis (DA), logistic regressio (LR), d multiomil logistic regressio (MLR) to distiguish solvecy positio ito two cses; two-clss clssifictio (helthy d isolvecy) d multi-clss clssifictio (helthy, merged, d isolvecy). The pper preseted the effects of solvecy positio of isurce compies. Compy d regultory ctios re required if compy s solvecy positio flls below requiremet. Due to the imblced dt problem, especilly for isolvecy compies, LR d MLR filed to give relible results. DA model ws ble to dequtely clssify Helthy, Merged, Isolvecy compies; 93.5%, 33.3% d 00% respectively (o the 998 dt set). 2. A Simple Approch to Ordil Frk d Hll (200) [7] preseted ordil clssifictio pproch tht ebles stdrd clssifictio lgorithms to clssify the ordil clss problems. Frk d Hll pplied stdrd clssifier i cojuctio with decisio tree lerer. The uderlyig lerig lgorithm tkes dvtge of ordered clss vlues. First, the origil dtset problem is trsformed from k-clss V = {v. v k } to k - biry-clss problems. The triig strts by derivig ew dtsets from the origil dtset, oe for ech of the k- ew clss ttributes. I the ext step, the clssifictio lgorithm is pplied to geerte model for ech of the ew dtsets. To predict the clss vlue of usee istce, we eed to estimte the probbilities of the k origil ordil clsses usig our k- model. Estimtio of the probbility for the first d lst ordil clss vlue depeds o sigle clssifier. I Geerl, for clss vlues V i, probbilities distributio o V i (k-clsses) is the derived s follows: Pr (V ) = - Pr (Trget > V) Pr (V i ) = mx { Pr (Trget > V i- ) Pr (Trget > V i ), 0 }, < i < k Pr (V k ) = - Pr (Trget > V k- ) To clssify istce of ukow clss, the istce is evluted by ech of the k- clssifiers d the probbilities of ech the k ordil clss vlue is clculted usig method bove. The clss with mximum probbility is ssiged to tht istce. 2.2 Decisio Tree Lerig Algorithm The Decisio Tree Lerig (DTL) lgorithm we used i this reserch is the oe med J48 implemeted i WEKA mchie lerig tool [8]. The J48 clss is implemeted bsed o the sme cocept s C4.5 decisio tree [9]. The DTL is predictive mchie lerig model which begis with set of the whole triig exmples. It cretes decisio tree bsed o the ttribute vlues of the triig dt tht c best clssify the set of smples t time. The ttribute which c best discrimite the smple set is evluted bsed o the cocept of Etropy. The exmples re the divided ito edges which is the vlue of the ttribute. The child ode which cosists of exmples from differet clsses will be replced with the ew ttribute ode, while the child ode cotiig exmples from the sme clss will be used s decisio ode, i which ll exmples will be clssified s the clss of triig exmples collected i this ode. 3. Dt d Methodology The dt set used i this study ws collected from 70 olife isurce compies i Thild. The compies which were i opertio or wet isolvecy were covered from 2000 to Durig this period, 66 cses (543 strog, 6 moderte, 3 wek d 44 isolvecy) were selected s triig dt set s show i Tble 2. The dt of yer 2009

3 364 TABLE 2 Number of No-life Isurce compies i this study (Dt from yer 2009 re the seprted test set). Clss Totl % 2009 Isolvecy % 6 Wek % Moderte % Strog % 57 Totl % 65 Note: The solvecy coditio i this study is determied by cpitl dequcy rtio = Totl cpitl vilble (TCA) / Totl cpitl required (TCR) were used s seprted test set. The dt source comes from the ul report of The Office of Isurce Commissio (OIC) d the helth isurce compies re ot icludig o this study The ttributes selectio strted from 3 ttributes. We chose them from the most commoly used oes i empiricl studies of isurce sciece. They were foud sigifict i previous studies of predictig o-life isurces solvecy [-, 3-6]. I this pper, we select the relevt ttributes usig the correltio-bsed ttribute subset evlutor d greedy stepwise. All 3 ttributed re show i Tble 3. TABLE 3 Attributes used i this study V Net premiums writte / policyholders surplus V2 Solvecy mrgi to miimum required solvecy mrgi V3 Policyholders surplus & Techicl reserve to et writte premium V4 Clims icurred to policyholders surplus & techicl reserve V5 Gross get s blce to policyholders surplus V6 Chge i policyholders surplus V7 Ivestmet yield V8 Ivestmet ssets to Policyholders surplus V9 Retur o totl ssets (ROA) V0 Lo & other ivestmet to policyholders surplus V Loss reserve & upid losses to policyholders surplus V2 Cpitliztio rtio V3 Auto lies et writte premium to totl et writte premium After we lyzed the distributio of the triig dt, we foud tht the distributio of the dt set ws imblced, s show i Tble 2. The clssifictio of dt with imblced clss distributio hs posed sigifict drwbck o the performce of most stdrd clssifiers, which ssume reltively blced clss distributio d equl misclssifictio costs [20]. My techiques were proposed to solve this problem, for exmple, re-smplig methods for the blcig the dt set, modifictio of existig lerig lgorithms, mesurig the clssifier performce i imblce domis, reltioship betwee clss imblce, d other dt complexity chrcteristics [2]. To ttck the imblced dt set problem, we employ the stdrd resmple techique to produce ew rdom set of dt by smplig with replcemet. The distributio o the dt sets fter pplyig resmple techiques is preseted i Tble 4. I this study, we use the ordil clss clssifier which employs the DTL lgorithm s the bse clssifier. Figure shows the clssifictio process. Fig. 2 d 3 shows the cocept of testig pproches, 0 fold crossvlidtios d 70:30% split dt set vlidtio. TABLE 4 Triig dt set fter pplyig resmple techique. Origil dt set Resmple dt set Clss Isolvecy % % Wek 3 2.% % Moderte 7 2.8% % Strog % % Totl % % Fig. Model Costructio.

4 365 Totl umber of exmples TABLE 7 results from test set (2009 dt set, 65 istces i totl) Experimet Experimet 2 Experimet 9 Experimet 0 Triig Test exmple Fig.2 0-fold cross-vlidtio Totl umber of exmples 70% Triig set 30% Test set Fig.3 70:30% Split dt set Clss I W M S Totl I = isolvecy, W = wek, M= moderte, S= strog Clssified Correctly I % W % M % S % Totl % The results of pplyig the ordil clss clssifier d DTL lgorithms o the dt itroduced bove deped o our selected ficil rtios (ttributes). The model shows good performce d correctly clssifies 98.7% from 0- fold cross-vlidtio, 95.7% from 30% spilt test set, d 92.3% from the seprted test set. The model c clssify the miority clss well but fil to recogize isolvecy clss i the seprted test set (66.7% correctly clssify). The reltive importce of ech ttribute (iput vrible) is lyzed by clcultig the wek clss of the reltioship betwee ech iput d output ttribute. 4. Experimetl d Results This pper used 0 fold cross-vlidtio, 30% split test set d seprted test set (2009 dt set). The clssifictio results re show i Tble 5, 6, d 7. TABLE 5 results obtied from 0-fold cross-vlidtio (totl 66 istces) Clss I W M S Totl I = isolvecy, W = wek, M= moderte, S= strog TABLE 6 results from 30% spilt test set (totl 85 istces) I = isolvecy, W = wek, M= moderte, S= strog Clssifie d Correctly I % W % M % S % Totl % Clssified Clss I W M S Totl Correctly I % W % M % S % Totl % TABLE 8 Performce evlutio mesure Evlutio Cross-vlidtio method MAE RMSE 0 fold cross-vlidtio % spilt test set Test set (2009 dt set) MAE- Me bsolute error RMSE- Root me squred error Tble 8 presets performce evlutio mesure of umeric predictio. I this study, we evluted the performce of predictio by MAE d RMSE. The MAE d RMSE re give by Me bsolute error (MAE) p =... Root me squred error (RMSE) p 2 2 = p... p Where, P,P 2.,.., P deote the predicted vlues o the test istces d, 2.,.., deote the ctul vlues. 5. Coclusios From the experimet settig d results reported i the previous sectio, the results idicte tht the obtied model c solve the problems of the multi-clss clssifictio d

5 366 lso the imblced dt set. I this study, we employ the ordil clss clssifier to solve the multi-clss problem, so tht our model c clssify the solvecy coditio of Thi No-life isurce compies ito four cses, strog, moderte, wek, d isolvecy. To ttck the problem of imblced dt set, we use the stdrd resmple techique which c highly improve the ccurcy of the miority clss which is the clss tht we re iterested. Our fil model re useful for isurce regultors, uditors, ivestors, mgemet, policy holders, d relted prty to determie the priority for further exmitios s erly wrig system. I our further reserch, we will pply the esemble methods d stdrd clssifiers proposed here to better improve the imblced dt set problem. Refereces [] P. Georgios, A Overview of Solvecy Supervisio, Regultios d Isolvecy predictio, Belgi Acturil Jourl, Vol. 8, 2009, pp [2] H. Scott, d N. Jck M., A Regressio-Bsed Methodology for Solvecy Surveillce i the Property-Libility Isurce Idustry, The Jourl of Risk d Isurce, Vol. 53, 986, pp [3] T. Jmes S., d P. George E., A Multivrite Model for Predictig Ficilly Distressed Property- Libility Isurce, The Jourl of risk d Isurce, Vol.40, 973, pp [4] A. J Mills, d S. J. Alle, Usig Best's Rtigs, Ficil rtio d prior probbilities i solvecy predictio, The Jourl of Risk d Isurce, Vol.55, 988. pp [5] C. Jmes M., d H. Robert E., Life Isurer Ficil Distress: Models d Empiricl Evidece, The Jourl of Risk d Isurce, Vol.62, 995, pp [6] C. J. Dvid, G. Mrti F., d P. Richrd D., Regultory Solvecy Predictio i Property-Libility Isurce: Risk-Bsed Cpitl, Audit Rtios, d Csh Flow Simultio, The Jourl of Risk d Isurce, Vol.66, No.3, 998, pp [7] B. R, d H. Robert A., Clssifyig Ficil Distress i the Life Isurce Idustry, The Jourl of Risk d Isurce, Vol.57, 990, pp [8] A. J M., d C. Ae M., Usig Best's Rtigs i Life Isurer Isolvecy Predictio, The Jourl of Risk d Isurce, Vol. 6, 994, pp [9] L. Suk Hu, d U. Jorge L., Alysis d Predictio of Isolvecy i the Property-Libility Isurce Idustry: A Compriso of Logit d Hzrd Models, Jourl of Risk d Isurce, Vol.63, 996, pp [0] B. R, d H. Joh, The Merger or Isolvecy Altertive i the Isurce Idustry, The Jourl of Risk d Isurce, Vol.64, 997, pp [] E.H. Duett, d R.A. Hershbrger, Idetifyig Ficil Distress i the Property-Csulty Idustry, Jourl of the Society of Isurce Reserch, Vol.2, 990, pp [2] C.S. Hug, R.E. Dorsey, d M.A. Boose, Life Isurer Ficil Distress Predictio: A Neurl Network Model, Jourl of Isurce Regultio, Vol.3, 994, pp [3] B. Ptrick L., C. Willim W., G. Lid L., d P. Uti, A Neurl Network Method for Obtiig Erly Wrig of Isurer Isolvecy, The Jourl of Risk d Isurce, Vol. 6, 994, pp [4] K. Bert, N.E.W.S.: A model for the evlutio of o-life isurce compies, Europe Jourl of Opertiol Reserch, Vol. 98, 997, pp [5] H. Shu-Hu, d W. Thou-je, A study of ficil isolvecy predictio model for life isurers. Expert Systems with Applictios, Vol.36, 2009, pp [6] S.S. Scho, F.V. Jose-Luise, S.V. Mri Jesus, B.C. Clos, Geetic progrmmig for the predictio of isolvecy i o-life isurce compies, Computers & Opertios Reserch, Vol. 32, 2005, pp [7] F. Eibe, d H. Mrk, A simple pproch to ordil clssifictio. I L. de Redt, & P. A. Flch (Eds.), Proceedigs of the Twelfth Europe Coferece o Mchie Lerig, 200, pp [8] H. Mrk, F. Eibe, H. Geoffrey, P. Berhrd, R. Peter, d W. I H., 'The WEKA Dt Miig Softwre: A Updte', SIGKDD Explortios Vol., Issue [9] J.R. Quil, C4.5: Progrms for Mchie Lerig. Morg Kufm Publishers Ic., 993. [20] S. Ymi., K. Mohmed S., W. Adrew KC., W. Yg, Cost-sesitive boostig for clssifictio of imblced dt Ptter Recogitio, Vol.40, 2007, pp [2] V. Grci, J.S. Sáchez, R.A. Mollied, R. Alejo, J.M. Sotoc, The clss imblce problem i ptter clssifictio d lerig, 2007, pp