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

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.