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Cost-of-Capital Margin for a General Insurance Liability Runoff

Published online by Cambridge University Press:  09 August 2013

Robert Salzmann  and
Mario V. Wüthrich
Robert Salzmann
Affiliation:
ETH Zurich, Department of Mathematics, 8092 Zurich, Switzerland
Mario V. Wüthrich
Affiliation:
ETH Zurich, Department of Mathematics, 8092 Zurich, Switzerland
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Abstract

Under new solvency regulations, general insurance companies need to calculate a risk margin to cover possible shortfalls in their liability runoff. A popular approach for the calculation of the risk margin is the so-called cost-of-capital approach. A comprehensive cost-of-capital approach involves the consideration of multiperiod risk measures. Because multiperiod risk measures are rather complex mathematical objects, various proxies are used to estimate this risk margin. Of course, the use of proxies and the study of their quality raises many questions, see IAA position paper [8]. In the present paper we provide a first discourse on multiperiod solvency considerations for a general insurance liability runoff. Within a chain ladder framework, we derive analytic formulas for the risk margin which allow to compare the comprehensive approach to the different proxies used in practice. Moreover, a case study investigates and answers questions raised in [8].

Keywords

Solvencyrisk margincost-of-capital approachmultiperiod risk measurerisk bearing capitalgeneral insurance runoffclaims reservingoutstanding loss liabilitiesclaims development resultchain ladder model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 415 - 451
Copyright
Copyright © International Actuarial Association 2010

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