Exponential utility maximization for an insurer with time-inconsistent preferences |
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| Institution: | 1. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, 201620, China;2. School of Statistics, East China Normal University, Shanghai, 200241, China;1. CEREMADE, Université Paris-Dauphine, France;2. Department of Agricultural and Resource Economics, University of California, Berkeley, United States;3. Ragnar Frisch Center for Economic Research, Oslo, Norway;4. Fisheries Centre, University of British Columbia, Vancouver, Canada;1. University of Southern California, Department of Mathematics, United States;2. CMAP, Ecole Polytechnique Paris, France;2. Department of Organic Chemistry, Faculty of Science, Autónoma University of Madrid, c/Francisco Tomás y Valiente 7, 28049 Madrid, Spain;3. IMDEA-Nanociencia, c/Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain |
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| Abstract: | This paper studies the optimal consumption–investment–reinsurance problem for an insurer with a general discount function and exponential utility function in a non-Markovian model. The appreciation rate and volatility of the stock, the premium rate and volatility of the risk process of the insurer are assumed to be adapted stochastic processes, while the interest rate is assumed to be deterministic. The object is to maximize the utility of intertemporal consumption and terminal wealth. By the method of multi-person differential game, we show that the time-consistent equilibrium strategy and the corresponding equilibrium value function can be characterized by the unique solutions of a BSDE and an integral equation. Under appropriate conditions, we show that this integral equation admits a unique solution. Furthermore, we compare the time-consistent equilibrium strategies with the optimal strategy for exponential discount function, and with the strategies for naive insurers in two special cases. |
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| Keywords: | Consumption–investment–reinsurance strategy Time inconsistence Equilibrium strategy Backward stochastic differential equation Integral equation |
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