Claims Provisions

FSAP Actuarial Valuation of General Insurance Claims Provisions Instituto de Seguros de Portugal 01/02/2006 Claims Provisions Summary Underlying principles Information reported by insurance undertakings Supervisory process 3.1 Ratio Analysis 3.2 Statistical Approaches Responsible actuaries practice Claims Provisions Underlying principles • Adequate claims provisions are essential for the financial soundness of general insurance companies • Claims provisions should correspond to a reasonably conservative estimate of the amount of future payments arising from claims incurred before the valuation date: Claims Reported to the insurance company Claims Incurred but Not Reported (IBNR) Claims Management Costs • Statistical methods are commonly used for the estimation of claims provisions Claims Provisions Information reported by insurance undertakings • ISP supervisory analysis is based on:  Responsible Actuary’s report  Auditor’s appraisal  Run-off triangles (claims paid, claims provision, number of claims) for main LOB’s:  Motor (also by coverage)  Property claims  Liability claims  Workers’ compensation  Temporary incapacity  Long-term assistance  Health  Individual insurance  Group insurance  Other relevant statistical data (e.g premiums, number of policies, Claims settlement expenses, etc.) • Data quality is crucial Claims Provisions ISP Supervisory Process • ISP pays particular attention to the responsible actuary’s critical analysis of the claims provision estimates • Several ratios are computed and analysed • ISP runs various statistical methods (deterministic and stochastic) to estimate the expected value and variability of the claims provision • A detailed technical and practical manual is available to ISP supervision staff as a guidance for the analysis of claims provisioning (off-site and on-site analysis) Claims Provisions 3.1 Ratio Analysis • Ratios and indicators considered on ISP analysis of claims provisions:  Growth on Premiums  Average Premium  Loss Ratio  Average Cost of New Claims  Average Claims Provision  Claims Frequency  Development of Claims Payments  “Speed” of Process closure  Re-openings  Claims Expenses  Provisioning, including IBNR  Readjustments • Ratios are calculated individually and compared on a static and evolutionary perspective with peer group and market benchmarks Claims Provisions 3.2 Statistical Approaches • The statistical methods’ objective is to project the expected future claims experience, using assumptions based on past data analysis complemented with expert opinion • The analysis should consist of:  Analysis of results (particularly the estimation error), taking into account the theoretical assumptions underlying each model  Analysis of relevant graphs and hypothesis tests to assess each models’ fitness Claims Provisions 3.2 Statistical Approaches (cont.) • Format of a Run-off triangle representing accident year x development year • Run-off triangles may refer to:  Number of claims  Claims paid (common approach)  Claims incurred, i.e Claims paid + Claims provision Accident year • Aim is to estimate the lower unknown triangle (shaded): Development year 1997 1998 1999 2000 2001 2002 2003 2004 2005 45.591 48.639 50.007 53.871 55.158 49.106 51.372 53.832 50.825 17.534 20.062 28.797 30.759 29.658 30.203 28.112 27.492 5.430 5.460 7.722 7.750 8.802 7.369 7.501 4.700 3.988 6.474 5.121 5.297 7.250 3.486 3.655 5.269 4.205 5.189 2.821 4.556 4.859 5.725 3.590 2.390 4.074 2.728 2.740 2.003 >8 1.358 (m.u.: thousand euros) Claims Provisions 3.2 Statistical Approaches (cont.) • Deterministic methods  Projection of past claims experience assuming fixed development factors  Provides point estimates of the expected future claims amounts  Various actuarial techniques are available • Stochastic models  Random nature of variables is considered  Generally speaking, the future claims amounts are assumed to follow a specified probability distribution  Allows for the measurement of the estimates variability, essential for the construction of confidence intervals for the estimates  Various actuarial models are available Claims Provisions 3.2 Statistical Approaches (cont.) Statistical Methods available at ISP • ISP has in-house built programs that allow for the automatic testing of the following statistical methods: Deterministic Stochastic Grossing Up Thomas Mack Model Link Ratio Generalised Linear Models: Chain-Ladder Over-dispersed Poisson Taylor Gamma Loss Ratio Inverse Gaussian Bornhuetter-Ferguson Loglinear Model (Kremer) Stress Testing Bootstrap simulation (VaR and Tail VaR calculations) • Some of the methods consider:  Possibility for inflation correction  Variant approaches based on different assumptions  Advanced refinements to include reparameterization and expert opinion Claims Provisions 3.2 Statistical Approaches (cont.) Statistical Approaches – Example • Results from running the programs for the previous run-off triangle: Provision held Best Estim ate Estim Error Estim Error (%) BE BE Sufficiency Sufficiency (%) Suffic Probab Norm al Suffic Probab Lognorm al DETERMINISTIC Grossing Up - Average 198.594 183.294 15.300 8% Link Ratio - Average 198.594 183.760 14.834 8% Grossing Up - Weighted 198.594 183.294 15.300 8% Link Ratio - Weighted 198.594 183.760 14.834 8% Chain Ladder - no inflation 198.594 184.319 14.275 8% Chain Ladder - w / inflation 198.594 184.624 13.970 8% Mack's Model 198.594 184.319 8.644 5% 14.275 8% 95% 95% ODP 198.594 184.319 13.121 7% 14.275 8% 86% 86% ODP - Bootstrap 198.594 184.319 13.751 7% 14.275 8% 85% 85% Gamma 198.594 188.328 12.367 7% 10.266 5% 80% 80% Gamma - Bootstrap 198.594 188.328 12.415 7% 10.266 5% 80% 80% Inv Gauss 198.594 189.225 28.180 15% 9.368 5% 63% 66% Inv Gauss - Bootstrap 198.594 189.225 28.699 15% 9.368 5% 63% 65% Loglinear 198.594 191.399 12.850 7% 7.195 4% 71% 72% Loglinear - Bootstrap 198.594 191.399 12.917 7% 7.195 4% 71% 72% STOCHASTIC m.u.: thousand euros 232.013 229.151 226.290 223.429 220.568 217.707 214.846 211.985 209.124 206.263 203.402 200.541 197.679 194.818 191.957 189.096 186.235 183.374 180.513 177.652 174.791 171.930 169.069 166.207 163.346 160.485 157.624 154.763 151.902 149.041 146.180 143.319 140.458 137.597 Claims Provisions 3.2 Statistical Approaches (cont.) Statistical Approaches – Example (cont.) • Simulated empirical distribution of the total claims provision using Bootstrap ODP stochastic model: 350 300 250 200 150 100 50 Claims Provisions 3.2 Statistical Approaches (cont.) Statistical Approaches – Example (cont.) • Goodness-of-fit tests for the Analytic ODP stochastic model: Test: Significance of model Parâm Estim M 10,62361766 A1998 0,063261536 A1999 0,253050203 A2000 0,291874246 A2001 0,309298151 A2002 0,254721372 A2003 0,241283213 A2004 0,262774653 A2005 0,212529774 B1 -0,65074148 B2 -1,956979381 B3 -2,218541598 B4 -2,434593748 B5 -2,373562924 B6 -2,617893165 B7 -2,74215242 B8 -3,021378097 B9 -3,410210981 parameters EP 0,048932988 0,063706426 0,061666529 0,061832402 0,062455212 0,064085587 0,065434972 0,066738007 0,077018058 0,03587058 0,063860539 0,077551497 0,09410069 0,10359585 0,137099385 0,184910402 0,303590867 0,367195751 % 0,46% 100,70% 24,37% 21,18% 20,19% 25,16% 27,12% 25,40% 36,24% 5,51% 3,26% 3,50% 3,87% 4,36% 5,24% 6,74% 10,05% 10,77% W 47134,76939 0,98608188 16,83892524 22,28226398 24,52546637 15,79828854 13,59672679 15,50316883 7,614728641 329,1093138 939,09028 818,3795636 669,3717645 524,9486045 364,6135692 219,9178577 99,04504351 86,25160822 Nív Sig.: X^2(1) 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 3,841455338 5,00% Decisão Par Não Nulo Par Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo Par Não Nulo P-value 0,00% 32,07% 0,00% 0,00% 0,00% 0,01% 0,02% 0,01% 0,58% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% 0,00% Claims Provisions 3.2 Statistical Approaches (cont.) Statistical Approaches – Example (cont.) Test: Assumption of normality of residuals y = 1,038x - 0,007 R2 = 0,9774 -2,5 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5 -1 -2 -3 3,0000 Test: Trends on residuals per development year 2,0000 1,0000 0,0000 -1,0000 -2,0000 -3,0000 > Claims Provisions Responsible actuaries practice • The company’s responsible actuary is expected to perform regular valuations of technical provisions (including claims provisions), using whatever methods he considers to be more reasonable • The analysis performed by responsible actuaries involves, in most cases, the use of deterministic methods and, increasingly, the use of stochastic methods • ISP recommendations: • • • • Enhancement of the quality of the information Estimation of the provision for management costs Encouragement for the use of stochastic models Highlight on the importance of testing the assumptions underlying each particular model – there is not an optimal model adjusted for all situations Claims Provisions Risk oriented approach The supervisory process of claims provisions analysis provides one important input for the global risk oriented framework