Optimal investment,consumption and proportional reinsurance for an insurer with option type payoff |
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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. Department of Statistics, Razi University, Kermanshah, Iran;2. Department of AFI-Insurance, KU Leuven, Leuven, Belgium;1. Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain;2. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain;3. Institute of Mathematics, Ufa Science Center of RAS, 112, Chernyshevsky Str., Ufa 450077, Russia |
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| Abstract: | This paper is devoted to the study of optimization of investment, consumption and proportional reinsurance for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximization. The surplus process of the insurer and the financial risky asset process are assumed to be diffusion processes driven by Brownian motions which are non-Markovian in general. Very general constraints are imposed on the investment and the proportional reinsurance processes. Based on the martingale optimization principle, we use BSDE and BMO martingale techniques to derive the optimal strategy and the optimal value function. Some interesting particular cases are studied in which the explicit expressions for the optimal strategy are given by using the Malliavin calculus. |
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| Keywords: | Investment Consumption Reinsurance Backward stochastic differential equation Malliavin calculus |
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