Open AccessOptimal investment and proportional reinsurance strategy under the mean-reverting Ornstein-Uhlenbeck process and net profit condition
Author(s) -
Yin Li,
Xuerong Mao,
Yazhi Song,
Jing Tao
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2020143
Subject(s) - reinsurance , ornstein–uhlenbeck process , economics , mean reversion , bellman equation , compound poisson process , econometrics , mathematics , poisson distribution , stochastic process , mathematical economics , actuarial science , poisson process , statistics
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.