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Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process

Zhibin Liang, Kam Chuen Yuen and Junyi Guo

Insurance: Mathematics and Economics, 2011, vol. 49, issue 2, 207-215

Abstract: In this paper, we study the optimal investment and proportional reinsurance strategy when an insurance company wishes to maximize the expected exponential utility of the terminal wealth. It is assumed that the instantaneous rate of investment return follows an Ornstein-Uhlenbeck process. Using stochastic control theory and Hamilton-Jacobi-Bellman equations, explicit expressions for the optimal strategy and value function are derived not only for the compound Poisson risk model but also for the Brownian motion risk model. Further, we investigate the partially observable optimization problem, and also obtain explicit expressions for the optimal results.

Keywords: Stochastic; control; Hamilton-Jacobi-Bellman; equation; Ornstein-Uhlenbeck; process; Compound; Poisson; process; Brownian; motion; Exponential; utility; Filtering; Partial; observations; Proportional; reinsurance; Investment (search for similar items in EconPapers)
Date: 2011
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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