NonTraditional Reserving Methods: Back to Basics

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Non-Traditional Reserving Methods Back to Basics

• Rajesh Sahasrabuddhe
• Aon Risk Consultants
• Midwestern Actuarial Forum
• Friday March 17, 2006

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Agenda

• Motivation
• Just One Example
• Questions and Answers

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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?

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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 dont 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.

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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.

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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
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True IBNR

• True IBNR is estimated using a frequency x
  severity approach
• Why? - This model is the most consistent with the
  real world!

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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)

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Report Lag

• The lag experience is truncated from above
• Similar to a deductible problem in reverse (Hogg
  Klugman Klugman, Panjer, Wilmot)

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Report Lag

• Use Maximum Likelihood Techniques (Loss Models
  KPW)
• Use a B-F model

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Report Lag

• Use pattern to allocate to claims-made periods
• May also apply model to estimate lag between
  report and closing

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True IBNR Severity and Settlement Model

• Severity Model

Closed w/ Indemnity?
Indemnity Model
Yes
No
Exp. Only Model
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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

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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)

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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

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Simulation (Part 1)

• Model the entire claims process

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Simulation (Part 2)

• Model the entire claims process

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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

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Questions and Answers