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Quasi Risk-Neutral Pricing in Insurance

Published online by Cambridge University Press:  09 August 2013

Harry Niederau  and
Peter Zweifel
Harry Niederau
Affiliation:
Dr. Niederau Consulting & Research, Hochstrasse 26, 8044 Zurich, Switzerland, E-mail: [email protected], Tel.: +41 43 537 03 51, Fax: +41 43 537 07 49
Peter Zweifel
Affiliation:
Socioeconomic Institute of the University of Zurich, Hottingerstrasse 10, 8032 Zurich, Switzerland, E-mail: [email protected], Tel.: +41 44 634 22 05, Fax: +41 44 634 49 07
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Abstract

This contribution shows that for certain classes of insurance risks, pricing can be based on expected values under a probability measure ℙ* amounting to quasi risk-neutral pricing. This probability measure is unique and optimal in the sense of minimizing the relative entropy with respect to the actuarial probability measure ℙ, which is a common approach in the case of incomplete markets. After expounding the key elements of this theory, an application to a set of industrial property risks is developed, assuming that the severity of losses can be modeled by “Swiss Re Exposure Curves”, as discussed by Bernegger (1997). These curves belong to a parametric family of distribution functions commonly used by pricing actuaries. The quasi risk-neutral pricing approach not only yields risk exposure specific premiums but also Risk Adjusted Capital (RAC) values on the very same level of granularity. By way of contrast, the conventional determination of RAC is typically considered on a portfolio level only.

Keywords

Incomplete marketsinsurance pricesLorenz orderproperty risksquasi risk-neutral pricingrisk aversionrisk neutralityrisk managementRisk Adjusted Capital (RAC)
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 317 - 337
Copyright
Copyright © International Actuarial Association 2009

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