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Non-Traditional Reserving Methods: Back to Basics

Non-Traditional Reserving Methods: Back to Basics. Rajesh Sahasrabuddhe Aon Risk Consultants Midwestern Actuarial Forum Friday March 17, 2006. Agenda. Motivation Just One Example Questions and Answers. Motivation. Non-Traditional = Back to Basics: How can this be?

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Non-Traditional Reserving Methods: Back to Basics

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  1. Non-Traditional Reserving Methods: Back to Basics Rajesh Sahasrabuddhe Aon Risk Consultants Midwestern Actuarial Forum Friday March 17, 2006 MAF 2006-03-17

  2. Agenda • Motivation • Just One Example • Questions and Answers MAF 2006-03-17

  3. Motivation • Non-Traditional = Back to Basics: How can this be? • Exams 1-4: Actuarial Modeling: ∫, ∑, ∏, f(x), F(x), Simulation • Exams 5-9: Arithmetic Models: +, / , *, -, deterministic • Why do we have this disconnect • How do we define “traditional”? MAF 2006-03-17

  4. Motivation • The value proposition of traditional models: benefit v.s. cost • Zehnwirth / Barnett: • “The standard link ratio models carry assumptions not usually satisfied by the data” • That same paper was later published in the Proceedings with softer language: “Most loss arrays don’t satisfy the assumptions of standard link ratio techniques.” • Why: • What does the nature of claims-made and occurrence development patterns tell us? What is a model? • Consideration of Trend, Limits and Deductibles. • Information aggregated is information lost. • Maturity and predictive ability. MAF 2006-03-17

  5. Motivation • The value proposition of traditional models: benefit v.s. cost • The output of traditional (deterministic) models – is it good enough? • How do (will) stakeholders view the cost of actuarial models? • Management is becoming increasing quantitative. MAF 2006-03-17

  6. Timeline for Case Study Mar 31, 2001 Oct 1, 2001 Sep 30, 2002 Excess Insurance – All events reported Reserve Analysis – All events occurring SIR Loss Forecast – All events occurring MAF 2006-03-17

  7. True IBNR • True IBNR is estimated using a frequency x severity approach • Why? - This model is the most consistent with the real world! MAF 2006-03-17

  8. True IBNR Frequency • IBNR Frequency is a direct function of exposure, initial expected ultimate frequency and report lag - i.e. IBNR frequency should be estimated using a B-F approach • Critical Assumption – How long between accident occurrence and claim reporting – Use approach contained in Weissner – “Estimation of the Distribution of Report Lags by the Method of Maximum Likelihood” - Proceedings of the Casualty Actuarial Society (1978) • Frequency is simulated as a Poisson distribution (or Negative Binomial) MAF 2006-03-17

  9. Report Lag • The lag experience is truncated from above • Similar to a deductible problem in reverse (Hogg & Klugman; Klugman, Panjer,& Wilmot) MAF 2006-03-17

  10. Report Lag • Use Maximum Likelihood Techniques (“Loss Models” – KPW) • Use a B-F model MAF 2006-03-17

  11. Report Lag • Use pattern to allocate to claims-made periods • May also apply model to estimate lag between report and closing MAF 2006-03-17

  12. True IBNR Severity and Settlement Model • Severity Model Closed w/ Indemnity? Indemnity Model Yes No Exp. Only Model MAF 2006-03-17

  13. Severity and Settlements Models • Fit severity models using individual claim data • Myriad of references for estimating claim severity distributions. My personal suggestions are: • Klugman, Panjer, & Wilmot - Loss Models • Keatinge – Modeling Losses with the Mixed Exponential Distribution • Severity and Settlement models can be (should be?) conditional on report and / or closing lag • Model is typically multi-modal MAF 2006-03-17

  14. IBNER • IBNER may be estimated using: • Severity Models and Bayesian theory • Transition Matrices (Mahon paper) • Last Resort: Case reserve adequacy statistics for the insurance industry – claims made coverage triangles from A.M. Best. (not a good option) MAF 2006-03-17

  15. Loss Forecast and Excess Insurance Analysis • Through our True IBNR reserve analysis, we have already developed the parameters necessary for: the loss forecast and the excess insurance analysis! • So we simply extend to the prospective year; but separately capture the results MAF 2006-03-17

  16. Simulation (Part 1) • Model the entire claims process MAF 2006-03-17

  17. Simulation (Part 2) • Model the entire claims process MAF 2006-03-17

  18. Result • A model that is both flexible and robust • A model that makes sense – ties with the real world • A model that provides results of interest to stakeholders MAF 2006-03-17

  19. Questions and Answers MAF 2006-03-17

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