Journal
INSURANCE MATHEMATICS & ECONOMICS
Volume 49, Issue 2, Pages 207-215Publisher
ELSEVIER
DOI: 10.1016/j.insmatheco.2011.04.005
Keywords
Stochastic control; Hamilton-Jacobi-Bellman equation; Ornstein-Uhlenbeck process; Compound Poisson process; Brownian motion; Exponential utility; Filtering; Partial observations; Proportional reinsurance; Investment
Categories
Funding
- National Natural Science Foundation of China [10701082]
- Natural Science Foundation of the Jiangsu Higher Education Institutions of China [09KJB110004]
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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. (C) 2011 Elsevier B.V. All rights reserved.
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