Optimal Prevention-Reinsurance Strategies in Diffusion Approximation Risk Models

In this paper, we investigate optimal prevention (intervention) and proportional reinsurance policies based on a diffusion approximation. The insurer chooses two strategies to control claim risk exposure: transferring risk to the third party by buying reinsurance; decreasing the intensity λ of claims to λ(p). Under minimising the probability of ruin, using ing techniques of stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman(HJB) equation and solve it to derive the optimal prevention-reinsurance strategy and value function. The results show there is a certain correlation between the two strategies, both of which are influenced by reinsurance premium claim size. Generally, as reinsurance becomes more expensive, insurance companies are more inclined to implement preventive plan; on the contrary, insurance companies have higher requirements for the effectiveness of prevention plan and are therefore more inclined to transfer risks by reinsurance. Verification and a numerical example are given to prove and illustrate our results.