Optimal Reinsurance And Investment Under The Heston Model

In recent years, the problem of optimal reinsurance and investment has become an important issue in the study of insurance mathematics. It provides theoretical support and guidance for the daily business activities of the insurance company. Therefore it has the important theory significance and the reality on the research. The thesis of optimal reinsurance and investment strategy under Heston risk model is studied. There are two main results.First result aims to maximize the expected exponential utility of insurance company's and reinsurance company's wealth at terminal time. Assuming that the risk process is a jump diffusion risk model, the insurance company can purchase the proportional reinsurance, the insurance companies also can invest risk-free assets and risky assets. The risk assets' price processes is the Heston model. In addition, the reinsurance company can buy risk-free assets to reduce the risk. By the stochastic control theory, we establish Hamilton-Jacobi-Bellman(HJB) equation and obtain the optimal reinsurance and investment strategy of the insurance company and reinsurance company. Finally, numerical simulation is carried out to prove the impact of parameters on the optimal reinsurance and investment strategy.Second result studies the optimal reinsurance and investment strategy between a large insurance company and a small insurance company. The larger one has sufficient assets to buy a risk-free asset and a risky asset, it even can buy a certain proportion of reinsurance and acquire new business, and the small insurance company can transfer a part of the risk to reinsurance companies through purchase proportional reinsurance.By studying a zero-sum game, we use stochastic control theory, draw a Nash equilibrium strategy and analyze the influence of parameters on the equilibrium strategies and its economic meaning behind it.