# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020051

## Optimal mean-variance reinsurance in a financial market with stochastic rate of return

 1 College of Science, Civil Aviation University of China, Tianjin 300300, China 2 School of Mathematical Sciences, Nankai University, Tianjin 300071, China 3 School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China

* Corresponding author: Zhongyang Sun

Received  June 2019 Revised  December 2019 Published  March 2020

In this paper, we investigate the optimal investment and reinsurance strategies for a mean-variance insurer when the surplus process is represented by a Cramér-Lundberg model. It is assumed that the instantaneous rate of investment return is stochastic and follows an Ornstein-Uhlenbeck (OU) process, which could describe the features of bull and bear markets. To solve the mean-variance optimization problem, we adopt a backward stochastic differential equation (BSDE) approach and derive explicit expressions for both the efficient strategy and efficient frontier. Finally, numerical examples are presented to illustrate our results.

Citation: Yingxu Tian, Junyi Guo, Zhongyang Sun. Optimal mean-variance reinsurance in a financial market with stochastic rate of return. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020051
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##### References:
the path of OU process $m(t)$ with $\alpha = -0.04$ and $\beta = 0.03$
the optimal investment strategy with $\alpha = -0.04, \beta = 0.03$ and $\alpha = \beta = 0$
the optimal reinsurance strategy with $\alpha = -0.04, \beta = 0.03$ and $\alpha = \beta = 0$
the effect of $\alpha$ on the efficient frontier
the effect of $\lambda$ on the efficient frontier
the effect of $\eta$ on the efficient frontier
the effect of $r$ on the efficient frontier
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