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

Yin Li; Xuerong Mao; Yazhi Song; Jian Tao

doi:10.3934/jimo.2020143

Article Contents

2022, Volume 18, Issue 1: 75-93. Doi: 10.3934/jimo.2020143

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

1.
Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China
2.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
3.
Business School, Jiangsu Normal University, Jiangsu 221116, China
4.
Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, China

^* Corresponding author: Yin Li
^* Corresponding author: Yin Li

Received: August 31, 2018

Revised: January 31, 2020

Early access: September 2020

Published: January 2022

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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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Mathematics Subject Classification: Primary: 90B50, 93E20; Secondary: 91G80.

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Figure 1. The optimal proportional level $ {q^*}\left( t \right) $ with $ n = 0.2, n = 0.5, n = 1 $, respectively

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Figure 2. The optimal proportional level $ {q^*}\left( t \right) $ with $ \Lambda = 1, \Lambda = 1.2, \Lambda = 1.5 $, respectively

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