The Research of the Risk Models with Investment by the Stochastic Process and the Optimal Control Theory 

Author  LiuZuo 
Tutor  LiSuoPing 
School  Lanzhou University of Technology 
Course  Operational Research and Cybernetics 
Keywords  Risk model Probability of ruin Lundberg inequality Utility theory Strangle Ito formula HJB equation 
CLC  F830.59 
Type  Master's thesis 
Year  2008 
Downloads  270 
Quotes  1 
Based on the classic risk models and all types of promotional risk model based on excess capital for investment to improve the solvency of insurance companies to reduce the probability of ruin, thereby establishing a new model with investing more in line with actual. New model of this type with investment mainly from the following study: First, we study different distribution under the bankruptcy probability for this model: 1. Consider premiums arrives and claims obedience discrete compound Poisson distribution case Lundberg inequality and establish a dual compound Poisson model with investment and interference, discussed the nature of the model, its earnings steady incremental process and the numerical characteristics of the surplus process; ultimate ruin probability general expression of the probability of bankruptcy. In particular, we are also by numerical simulation described the ruin probability upper bounds, respectively, with the amount of investment, the premium of the insurance claim amounts movements. To more clearly reflect the changes in the relationship between each variable and ruin probability has good theoretical significance. 2 to consider premiums to reach the compound negative binomial distribution model and claims obedience. In this section, we have a twotier research first single insurance with investment and interference composite negative binomial model, double insurance with investment and interference composite negative binomial distribution model. And their nature were discussed its earnings steady incremental process and the numerical characteristics of the surplus process; access to the ultimate ruin probability Lundberg inequality and the general expression of the probability of bankruptcy. Secondly, we study the filtration process risk models consider the utility function and the discount factors. The model not only take into account the investment factors, but also joined the utility theory and the discount factor, which is rarely appear in other papers. In this part of the content, martingale, draw the upper bound of the ruin probability. For this filtration process more practical significance. Finally, we improved the model investment. Consider investing in riskfree investment, there is a part that can be used for risk investment. With this improvement will be the introduction of the securities market and theoretical risk theory, which is more in line with the direction of the development of the financial markets, and has a good practical significance. In this section, the main application of optimal control methods in stochastic control theory, the HJB equation model to find optimal investment strategy of the model, which can be further minimized, making the bankruptcy probability.