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Reinsurance Arrangements Minimizing the Risk-Adjusted Value of an Insurer's Liability

Published online by Cambridge University Press:  09 August 2013

Yichun Chi
Yichun Chi*
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China, E-mail: yichun_1982@hotmail.com
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Abstract

In this paper, we investigate the problem of purchasing a reinsurance policy that minimizes the risk-adjusted value of an insurer's liability, where the valuation is carried out using a cost-of-capital approach. In order to exclude the moral hazard, we assume that both the insurer and reinsurer are obligated to pay more for larger loss in a typical reinsurance treaty. Moreover, the reinsurance premium principle is assumed to satisfy three axioms: law invariance, risk loading and preserving convex order. The proposed class of premium principles is quite general in the sense that it contains all the widely used premium principles except Esscher principle listed in Young (2004). When capital at risk is measured by the value at risk (VaR) or conditional value at risk (CVaR), we find it is optimal for the insurer to cede two separate layers over the prescribed premium principles. By imposing an additional weak constraint on the premium principle, we further get that the reinsurance in the form of a layer is optimal. Finally, to illustrate the applicability of our results, we derive explicitly the optimal one-layer reinsurance for expected value principle and Wang's premium principle, and show that two-layer reinsurance may be optimal for Dutch premium principle.

Keywords

Capital at riskCost of capitalConditional value at riskValue at riskOptimal reinsuranceWang's premium principleDutch premium principleLayer reinsurance
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 2 , November 2012 , pp. 529 - 557
Copyright
Copyright © International Actuarial Association 2012

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