A Framework For Estimating Uncertainty in Insurance Claims Cost

Transcription

1 A Framework For Estimating Uncertainty in Insurance Claims Cost Conor O Dowd, Andrew Smith, Peter Hardy PricewaterhouseCoopers 2005 The Institute will ensure that all reproductions of the paper acknowledge the Author/s as the author/s, and include the above copyright statement:

2 Agenda Why do we need a framework? Proposed Framework Individual product group Inter-product group dependencies Insights & Lessons Learned

3 Why a Framework? Current Approaches have Limitations: Implied Need Separate approaches to mean, variance, covariance Bottom up approach little work done on risk aggregation (diversification benefit) Quantitative techniques for CoVs are costly, inconclusive and backward-looking No acknowledgement of subjective elements of the valuation basis Business information provided to the actuary Assumptions made by the actuary Consistent approach based on the underlying distributional form Portfolio approach based on estimating key uncertainties An approach that looks at all sources of variability in estimates A means of controlling and bringing accountability to Qualitative information provided to the actuary the use of subjective judgement by the actuary

4 The Framework in General Top-down approach to identifying key risks Identification Assessment Quantification Goal is to make sure all sources of risk are identified and key risks quantified To this end, hierarchical risk categories are used (this also enables identification of dependence relationships between risks) Has broad similarities with approaches being developed for operational risk quantification (eg. Basel II AMA)

5 Components of Risk Source of Risk Description Example Independent Risk Independent Parameter Process error in past data results Volatility in past results even if the Error in volatility in calibrating the model process does not change Process Error Future insurance process has Tossing of an unbiased coin 100 volatile outcomes relative to times will not always give 50 tails expected Systemic Risk Model Specification Model is an imperfect Actuarial model assumes payments Risk representation of complex related to simplistic predictor real-life processes - includes (finalised claims) while process is "systemic parameter error" more complex Future Systemic Risk Trends move systemically away Trends in inflation from current realistic outcomes

6 Product Group Framework Model Specification Risk Future Systemic Risk Independent Risk Model specification risk questionnaire Future system ic risk questionnaires, interviews, workshops Quantitative techniques Risk Identification G eneral M odelling A ppro ach A bility to rem odel A vailability & value of claim predictors B usiness knowledge utilisation D etection of trends Data errors & lim itations Recovery Claims settlement P ricing Re serving Sensitivity C laim s repo rting Underwriting Claims Incidence B ootstrappin g Conceptu al M odelling Hindsight M od elling Systemic Risk / Qualitative Fram ework Independent Risk / Quantitative Fram ework Risk Identification and Categorisation Risk Assessment Inadequate M is-specified D ata B usiness M od el Lim itations K nowledge Scored against best/worst case Claim s Inflation Risk E conom ic, Social risk C laim s Expense risk Event Risk C laim S everity R isk Recovery Risk P rocess Change Risk O the r Latent claim Risk Process Risk Param eter Risk Risk Quantification (Simulation Model) Model Specification Data Lim itations Future System ic Risk Independent Risk D istribution Stochastic sim ulation Product Group Claim Distribution

7 Independent Risk Risk Identification Quantitative techniques Formal modelling (eg. Bootstrapping), informal modelling (eg. Sensitivity analysis) and historic reserving variance Bootstrapping Quantitative techniques Hindsight Modelling Other Statistical Techniques Independent Risk / Quantitative Framework Risk Assessment Adjust results for major known systemic episodes Process Risk Parameter Risk Independent Risk Distribution

8 Model Specification Risk Risk Identification Mainly qualitative techniques used to compare valuation methods Consistency of approach across product groups Risk Assessment Balanced scorecard approach and use of risk indicators General Modelling Approach Ability to remodel Model specification risk questionnaire Mis-specified Model Availability & value of claim predictors Business knowledge utilisation Inadequate Business Knowledge Data Limitations Scored against best/worst case Detection of trends Data errors & limitations Calibration of model based on: - Actuarial model differences - Black box model outputs - Actuarial judgement!!! Model Specification Data Limitations

9 Future Systemic Risk Risk Identification Forward looking method Identify key risks by mapping business processes and interviews with business experts Future systemic risk questionnaires, interviews, workshops Recovery Claims settlement Pricing Reserving Sensitivity Underwriting Claims reporting Claims Incidence Risk Assessment Key risks categorised into independent risk buckets Risk Identification and Categorisation Claims Claim Severity Inflation Risk Risk Claims Expense risk Economic, Recovery Risk Social risk Event Risk Process Change Risk Other Latent claim Risk Quantification using mix of qualitative and quantitative techniques Future Systemic Risk

10 Inter-product Group Dependencies Risk categories identified gives power to measuring dependencies across different product groups Explicitly model root cause of dependencies For example event risk, inflation risk, data risk Explicit tail correlations can be separately identified and modelled If you can t identify dependencies then they probably don t exist Stochastic simulation techniques can be used to model resulting dependencies

11 Practical Application of Framework Asbestos portfolio: Qualitative investigations Interviews with business experts (medical, legal, actuarial etc) Sensitivity / scenario analysis under a probabilistic framework LMI portfolio: Mainly quantitative methods used Stochastic economic modelling E Kelly, K Smith (2005)

12 Practical Application of Framework Insurer with multiple lines of business: Mixture of quantitative and qualitative methods: Quantitative approach to independent risk and event risk Qualitative approach for model specification risk and other components of future systemic risk Consistency of assumptions across product groups: Economic risk effects related to the mean term of liabilities Model specification risk consistent method / quantification across product groups Root cause of dependencies identified and explicitly modelled

13 Insights & Lessons Learned Top few risks in a class often comprise over 90% of uncertainty Difficult to justify high correlations unless key risks or processes are shared Multiplier approach to premium liabilities is inherently flawed Some risks do not fall easily under commonly used distributions (eg events) Model specification risk is still a significant challenge requiring further work

14 Advantages of Proposed Framework A robust and forward looking framework Auditable, replicable and transparent process Consistency in: approach to moment estimation methods used between product groups and over time Premium liabilities treated appropriately No distributional limitations on risks or results Identification of key risks and control of subjectivity Dependencies explicitly identified and quantified