Reserving for Medical Professional Liability

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Reserving for MedicalProfessional Liability

• Casualty Loss Reserve Seminar
• September 10-11, 2001
• New Orleans, Louisiana
• Rajesh Sahasrabuddhe, FCAS, MAAA
• Aon Risk Consultants, Inc.

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Presentation of Model

• Motivation Rationale
• Theory via Case Study
• Mid level discussion with technical references
• Questions and Answers

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Motivation Rationale

• Zehnwirth / Barnett
• The standard link ratio models carry assumptions
  not usually satisfied by the data
• Why?
• SIRs on Occurrence Basis / Excess is often on a
  Claims-Made Basis

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Motivation Rationale

• A model easily adaptable to simulation techniques
• A Model that works with client data
• Many clients do not track triangles they simply
  have a loss run

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Our Experience with Reserving for HPL

• IBNER is generally minimal
• Case reserves, in the aggregate, tend to be
  reasonably adequate
• Most Healthcare institutions are conservative by
  nature
• The majority of cost stems from suits
• The rest is just noise
• Simulation is necessary
• To model alternative coverage programs
• To determine variability in results

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Reserve Analysis

• IBNR Liabilities are the sum of the following
• Incurred but not enough reported (IBNER)
• True Incurred but not reported
• Estimate Components Separately

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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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IBNER

• IBNER may be estimated using
• Case reserve adequacy statistics for the
  insurance industry claims made coverage
  triangles from A.M. Best
• Payment model large clients
• Last Reserve statistics
• Factors of IBNER / Reported Loss are simulated
• Dew and Hedges Reserving for Excess Layers

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True IBNRthe interesting part

• 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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Our Reserve Analysis 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)

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Report Lag

• The lag experience is truncated from above
• Similar to a deductible problem (Hogg Klugman)

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Report Lag

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

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True IBNR Frequency

• Use pattern to allocate to claims-made periods
• May also apply model to estimate lag between
  report and closing
• Frequency is simulated as a Poisson distribution

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True IBNR Severity

• Severity Model

Closed w/ Indemnity?
Indemnity Model
Yes
No
Exp. Only Model
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True IBNR Severity

• 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

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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
  clients

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Other considerations / future enhancements

• Basic losses / Shock Losses
• Model severity as a function of the report lag
• Separate severity distributions for lawsuits and
  claims
• Parameter Risk