Optimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition

Li, Yin and Mao, Xuerong and Song, Yazhi and Tao, Jian (2022) Optimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition. Journal of Industrial and Management Optimization, 18 (1). pp. 75-93. ISSN 1547-5816 (https://doi.org/10.3934/jimo.2020143)

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Abstract

In this study, under the criterion of maximizing the expected exponential utility of terminal wealth, the optimal proportional reinsurance and investment strategy for an insurer is examined with the compound Poisson claim process. To make the model more realistic, the price process of the risky asset is modelled by the Brownian motion risk model with dividends and transaction costs, where the instantaneous of investment return follows as a mean-reverting Ornstein-Uhlenbeck process. At the same time, the net profit condition and variance reinsurance premium principle are also considered. Using stochastic control theory, explicit expressions for the optimal policy and value function are derived, and various numerical examples are given to further demonstrate the effectiveness of the model.

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