Optimal reinsurance with regulatory initial capital and default risk |
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Institution: | 1. School of Finance, Zhongnan University of Economics and Law, Nanhu Road, Wuhan, PR China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong;3. School of Finance, Nankai University, Weijin Road, Tianjin, PR China;1. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong;2. Department of Mathematics, King’s College London, Strand, London, United Kingdom;3. Department of Statistics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong;1. Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada |
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Abstract: | In a reinsurance contract, a reinsurer promises to pay the part of the loss faced by an insurer in exchange for receiving a reinsurance premium from the insurer. However, the reinsurer may fail to pay the promised amount when the promised amount exceeds the reinsurer’s solvency. As a seller of a reinsurance contract, the initial capital or reserve of a reinsurer should meet some regulatory requirements. We assume that the initial capital or reserve of a reinsurer is regulated by the value-at-risk (VaR) of its promised indemnity. When the promised indemnity exceeds the total of the reinsurer’s initial capital and the reinsurance premium, the reinsurer may fail to pay the promised amount or default may occur. In the presence of the regulatory initial capital and the counterparty default risk, we investigate optimal reinsurance designs from an insurer’s point of view and derive optimal reinsurance strategies that maximize the expected utility of an insurer’s terminal wealth or minimize the VaR of an insurer’s total retained risk. It turns out that optimal reinsurance strategies in the presence of the regulatory initial capital and the counterparty default risk are different both from optimal reinsurance strategies in the absence of the counterparty default risk and from optimal reinsurance strategies in the presence of the counterparty default risk but without the regulatory initial capital. |
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Keywords: | Optimal reinsurance Reinsurance premium Value-at-risk Counterparty default risk Utility function Convex order |
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