Optimal reinsurance under dynamic VaR constraint |
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| Institution: | 1. School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW, Sydney NSW 2052, Australia;2. Département de Mathématiques et de Statistique, Université de Montréal, Montréal QC H3T 1J4, Canada;1. Faculty of Actuarial Science and Insurance, Cass Business School, London, United Kingdom;2. Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia;3. Department of Mathematics, Wayne State University, Detroit, MI 48202, United States;1. School of Insurance, Central University of Finance and Economics, Beijing 100081, China;2. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China;3. School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China;1. Amsterdam School of Economics, University of Amsterdam, Netherlands;2. Department of Accountancy, Tilburg University, CentER for Economic Research and Netspar, Netherlands;3. Department of Econometrics and OR, Tilburg University, CentER for Economic Research and Netspar, Netherlands;1. School of Business Administration, Hunan University, Changsha 410082, China;2. Business School, Hunan Normal University, Changsha 410081, China;3. Kent Business School, University of Kent, Canterbury, CT2 7PE, UK |
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| Abstract: | This paper deals with the optimal reinsurance strategy from an insurer’s point of view. Our objective is to find the optimal policy that maximises the insurer’s survival probability. To meet the requirement of regulators and provide a tool to risk management, we introduce the dynamic version of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and worst-case CVaR (wcCVaR) constraints in diffusion model and the risk measure limit is proportional to company’s surplus in hand. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. Applying dynamic programming technique, we obtain closed form expressions of the optimal reinsurance strategies and corresponding survival probabilities under both proportional and excess-of-loss reinsurance. Several numerical examples are provided to illustrate the impact caused by dynamic VaR/CVaR/wcCVaR limit in both types of reinsurance policy. |
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| Keywords: | HJB equation Dynamic Value-at-Risk (VaR) Conditional Value-at-Risk (CVaR) Worst-case CVaR (wcCVaR) Survival probability |
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