Investment Issues In The Classical Risk Process And The Dual Model

In recent years, insurance companies and other industries often require better management on market and operational risks due to severe competition. For insurance companies at the same time, in order to reduce the risk of large claims, the insurance company takes reinsurance policy for claims, and consider the problem of the reinsurance strategy. Therefore, there have arisen many optimization problems with various objectives in insurance risk management. While the research and study of these problems is benefit to the management and development of the enterprise.In this essay, we first analyze the case of insurance companies. We study the optimal investment and excess-of-loss reinsurance. We model risk process to classical risk model to study optimization problem of maximizing the utility of expected terminal surplus under the controls of excess-of-loss reinsurance and investment. Then, we study a number of other industries, which pay costs continuously and have occasional profits(that is, dual insurance risk model). Under this model, we also discuss the optimal investment strategy.In this essay, when we give a description of the model of the risky assets in the financial market, we abandon the classic Black-Scholes Geometric Brownian motion model and take the more realistic Oristein-Uhlenbeck model. This makes the process of stock price showing the characteristics of the bull and bear markets, which fit the real world more accurately.We use the stochastic control theory and solve the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Explicit forms for the optimal reinsurance-investment strategy and corresponding value function are obtained. It provides some good advice to insurance companies and other industries in the risk management and investment behavior.