Under The Dependent Risk Model Of The Optimal Reinsurance And Portfolio

Insurance company usually use reinsurance to spread risk and investment, increase profits, thus risk model of optimal control problem become a hot topic in the academic circles. In recent years, risk model has got a lot of research from different aspects, and also discussed about how danger is planted, but a lot of model only considered a single premium again without thinking about the investment market. About this sample hypothesis, the model is very limited in practical application. In practice, the insurance company will take reinsurance and investment to get more profits. So this article considers the optimal rein-surance and investment strategies of the model bases on the different premium principle and various investment markets. The mainly research of content is as follows:The first chapter, we simply sum up the research background and the latest research in the theory of risk dynamic.The second chapter, we mainly introduce the dependent risk model, index premium principle, excess loss risk premium principle and relate market price model.The third chapter, we base on the framework of diffusion dependent risk model,studies the optimal reinsurance and investment problem. There are two kinds of dependency claims process, and each claim is used excess loss reinsur-ance,and the insurance company can investment the asset to the market which is made up of no risk market and risk market, the risk market CEV process. Using the stochastic control theory, we get the analytic expression of optimal investment strategy, proves the existence and uniqueness of the optimal rein-surance strategy.The fourth chapter, we base on the framework of diffusion dependent risk model, insurance company uses the index premium principle to calculate the premium income, studies the optimal reinsurance and investment problem. Risky assets are characterized by Heston process, uses the theory of stochas-tic control, we get the analytic expression of optimal investment strategy and proves the existence and uniqueness of the optimal reinsurance strategy.The fifth chapter, we base on the framework of the jump dependent risk model, under the premium income of insurance company is calculated by the index premium principle, studies the optimal reinsurance and investment prob-lem. Risky assets is depicted by O - U process, using the stochastic control theory, we get the analytic expression of optimal investment strategy, and proves the existence and uniqueness of the optimal reinsurance strategy.