Pareto-optimal reinsurance arrangements under general model settings |
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| Institution: | 1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;3. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China;1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China;2. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China;3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1, Canada;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;1. Department of Finance, Beijing Technology and Business University, Beijing, 100048, China;2. Institute, Shenzhen Stock Exchange, Shenzhen, 518028, China;1. Department of Finance and Statistics, School of Management, University of Science and Technology of China, China;2. Department of Mathematics and Department of Statistics and Probability, Michigan State University, USA |
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| Abstract: | In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. For the purpose of practice, we use numerical examples to show how to determine the mutually acceptable Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer’s aim and the reinsurer’s goal can be met under the mutually acceptable Pareto-optimal reinsurance contracts. |
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| Keywords: | Pareto optimality Optimal reinsurance Comonotonic-semilinearity Comonotonic-convexity Tail-Value-at-Risk |
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