On The Optimal Investment Proportion On The Risk Model With Correlated Brownian Motion

In this thesis, we study the double-diffusion process risk models. We assume the surplus of the insurance company is described by diffusion process in the moment t , we noted by R t. In addition, the insurance company will put the surplus R t into the financial market according to the proportion b (∈[0,1]), i.e., we put bR t and Rt into risk market and risk-free market respectively, This moment the surplus of the insurance company R t will satisfied the following differential equation where the constantμ> 0 denotes net charge of insurance companies in unit time. r0≥0 denote the rate of capital which put into risk-free market. r1 > 0is the rate of capital expectations which put into risk market.σ0 ,σ1denotes Diffusion coefficient. is a Standard Brownian motion, which is used to describe surplus process R t,that is dR be another Standard Brownian motion standing for changes which caused by unpredictable factor in risk market. We denote the correlation coefficient of two Brownian motion byρ,that is In this thesis, we investigated the minimal ruin probability and the optimal investment proportion problems in the condition ofρ≠0, which is to search for the optimal proportion of the investment value b ,basing on making the ruin probability of the company minimum.We also discusses the dividends model. where Lt is the total dividends by time t. Using disturbance method, we obtain differential equation, which satisfied by the optimal dividends strategy and dividends function m ( u ), we obtain the numerical solution of dividends function m ( u ). Related graphic examples are also illustrated.