Impulse Control Model In Finance And Insurance And Analysis Of Its Property

In today’s society, financial economic market is very complex. People consider from the qualitative analysis to the quantitative analysis, more to the combination of the two. People in the financial markets also have a better understanding and control. Dividend is the fundamental problem of the insurance company. To the stockholder, Get dividend when the company have profit; injection when the company has deficit; For the insurance company, the bankrupt time is the right time to decide whether we should go bankrupt or financing to make the company survive long.With the development of the study, people invest from dividend、financing to the reinsurance. Discount rate is not fixed, but considering the regime and market rate.The paper consider the most important problem of financial insurance:dividend、equity issuance 、reinsurance control strategy and optimal dividend with the regime-switching. The main contents are in chapter 3 and In chapter 4:in chapter 3,in the frame work of general diffusion model,we study the reinsurance,put forward comprehensive control strategy with dividend,financing and reinsurance.the paper uses the application of dynamic programming principle and ito’s expression.get the value function which satisfied The HJB equation.According to the property of the value function,the HJB equation is transformed into the problem of a free boundary problem.and the paper can prove the solution of a free boundary problem is the value function of the stochastic control problem, get bonus points,capital and reinsurance strategy representation. In chapter 4,in the market of mode conversion,the paper has established the control model with dividends and financing,Derived the HJB equation,and then the paper gives the solution to value function.And the optimal control strategy.