Abstract:
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, and decreasing the intensity
λ of claims to
λ(
p). To minimize the probability of ruin, we employ techniques of stochastic control theory to establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation which is then solved to derive the optimal prevention-reinsurance strategy and value function. The results show that 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; conversely, 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.