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Catastrophe Modeling and Actuarial Applications. Jonathan Evans, FCAS, MAAA Actuary Iowa Actuarial Club February 23, 2007. What Are Catastrophes ?. Single events that produce such a large number of claims

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Catastrophe modeling and actuarial applications

Catastrophe Modeling and Actuarial Applications

Jonathan Evans, FCAS, MAAA


Iowa Actuarial Club

February 23, 2007


What are catastrophes
What Are Catastrophes ?

  • Single events that produce such a large number of claims

    – that it is very highly improbable such an event would actually occur (assuming risk exposures are independent)

  • Usually resulting from a special type of peril: hurricane, earthquake, terrorist attack, asbestos, etc.

  • More rarely, sometimes extremely large single claims are called “catastrophes”


What applications make actuaries care about catastrophes
What Applications Make Actuaries Care About Catastrophes ?

  • Ratemaking for policies exposed to catastrophes, such as homeowners in Florida

  • Reserving for long tail catastrophic losses, such as asbestos in general liability

  • Analyses of reinsurance programs

  • Analyses of insurer catastrophe risk, such as catastrophic return period loss estimates


Why model catastrophes
Why Model Catastrophes ?

  • For non-catastrophic perils (such as an automobile accident that independently affects risk exposures or only a few risk exposures simultaneously) it is easy to gather a credible volume of experience

  • For catastrophic perils (such as hurricanes) even nationwide experience over many years may not be credible


Who builds catastrophe models
Who Builds Catastrophe Models ?

  • Prior to the 1980s most models were built by insurers for underwriting purposes

  • From the 1980s to present most models were built by specialized modeling firms and sold as software, that allows users to input exposure information

  • Event databases and estimated frequencies are often prepared by scientists: geophysical for earthquake, atmospheric for hurricanes, social/behavioral for terrorism, etc.

  • Loss functions are often determined by engineers

  • Actuaries are mostly end users of models; except for reserving models for mass liability, such as asbestos/environmental, where actuaries have compiled databases and built their own models


How are catastrophes modeled
How Are Catastrophes Modeled ?

Catastrophe models generally consist of:

  • A database of individual exposures, such as homeowners policies by location and insured value

  • A database of potential catastrophic events, such as hurricanes by landfall location and wind speed

  • A loss function that uses as input the characteristics of a single exposure from #1 and a single catastrophic event from #2

  • Estimates for the frequency of each catastrophic event in #2


Example of calculating loss
Example Of Calculating Loss

For Policy A and Event U the loss is calculated as:


Further reading
Further Reading

-Bouska, Amy, “From Disability Income to Mega-Risks: Policy-Event Based Loss Estimation”, CAS Forum, Summer 1996.

-Grossi, Patricia and Kunreuther, Howard, Catastrophe Modeling: A New Approach to Managing Risk (Huebner International Series on Risk, Insurance and Economic Security),Springer, 2005.

-Kozlowski, Ronald T. and Mathewson, Stuart B., “Measuring and Managing Catastrophic Risk”, CAS Discussion Paper Program, 1995.

-Woo, Gordon, The Mathematics of Natural Catastrophes, World Scientific Publishing Company, 1999.