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Optimal investment,consumption and proportional reinsurance under model uncertainty |
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| Affiliation: | 1. Department of Statistics, Wuhan University of Technology, Wuhan, 430070, PR China;2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, PR China;1. Robert H. Smith School of Business, University of Maryland, United States;2. Department of Mathematics, Imperial College London, United Kingdom;3. Faculty of Mathematics and Economics, University of Ulm, Germany;1. School of Science, Tianjin Polytechnic University, Tianjin 300387, China;2. College of Management and Economics, Tianjin University, Tianjin 300072, China;3. School of Finance, Zhejiang University of Finance & Economics, Hangzhou 310018, China;1. Institut de recherche mathématiques de Rennes, Université de Rennes 1, 35042 Rennes Cedex, France;2. School of mathematical sciences, Shanghai Jiao Tong University, 200240 Shanghai, China;3. Centre de mathématiques appliquées, École Polytechnique, 91128 Palaiseau Cedex, France;4. Département de mathématiques, Université de Maradi, BP 465 Maradi, Niger |
| Abstract: | This paper considers the optimal investment, consumption and proportional reinsurance strategies for an insurer under model uncertainty. The surplus process of the insurer before investment and consumption is assumed to be a general jump–diffusion process. The financial market consists of one risk-free asset and one risky asset whose price process is also a general jump–diffusion process. We transform the problem equivalently into a two-person zero-sum forward–backward stochastic differential game driven by two-dimensional Lévy noises. The maximum principles for a general form of this game are established to solve our problem. Some special interesting cases are studied by using Malliavin calculus so as to give explicit expressions of the optimal strategies. |
| Keywords: | Investment Consumption Reinsurance Model uncertainty Stochastic maximum principle Malliavin calculus |
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