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

Yingxu Tian; Junyi Guo; Zhongyang Sun

doi:10.3934/jimo.2020051

Article Contents

2021, Volume 17, Issue 4: 1887-1912. Doi: 10.3934/jimo.2020051

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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
^* Corresponding author: Zhongyang Sun

Received: May 31, 2019

Revised: November 30, 2019

Early access: March 2020

Published: July 2021

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Abstract

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.

Keywords:

Investment-reinsurance strategy,
Rate of investment return,
Ornstein-Uhlenbeck process,
Backward stochastic differential equation,
Efficient frontier.

Mathematics Subject Classification: Primary: 93E20; Secondary: 91B30, 91G80.

Citation:

Full Text(HTML)

Figure 1. the path of OU process $ m(t) $ with $ \alpha = -0.04 $ and $ \beta = 0.03 $

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Figure 2. the optimal investment strategy with $ \alpha = -0.04, \beta = 0.03 $ and $ \alpha = \beta = 0 $

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Figure 3. the optimal reinsurance strategy with $ \alpha = -0.04, \beta = 0.03 $ and $ \alpha = \beta = 0 $

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Figure 4. the effect of $ \alpha $ on the efficient frontier

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Figure 5. the effect of $ \lambda $ on the efficient frontier

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Figure 6. the effect of $ \eta $ on the efficient frontier

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Figure 7. the effect of $ r $ on the efficient frontier

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