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Sharing Risk – An Economic Perspective

Published online by Cambridge University Press:  09 August 2013

Andreas Kull
Andreas Kull*
Affiliation:
AXA Winterthur, P.O. Box 357, CH-8401 Winterthur, Switzerland, E-mail: andreas.kull@axa-winterthur.ch
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Abstract

We revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

Keywords

Sharing and pooling of riskreinsuranceoptimal retentionsrisk-based capitalcapital cost
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 591 - 613
Copyright
Copyright © International Actuarial Association 2009

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