The Mean, Variance And Stochastic Differential Game Problem Is Studied  Posted on:20131213  Degree:Master  Type:Thesis  Country:China  Candidate:C H Zhang  Full Text:PDF  GTID:2249330374487589  Subject:Probability theory and mathematical statistics  Abstract/Summary:  PDF Full Text Request  Portfolio selection is a classic and important problem in financial economics. Together with asset pricing and risk management, portfolio selection are coined as three pillars in modern finance. An early scientific contribution to portfolio selection was made by the work of Markowitz, where an elegant mathematical model for portfolio selection was introduced. There are many uncertain events, such as inflation, disaster, wars and so on, which may influence the return rate and the volatility of the asset greatly. Therefore, it is necessary to introduce the more realistic model to represent the random variation of the environmental or economical condition. It has very important significance in theory and practial to study the strategy selection problem under the more realistic asset price model.In this paper we first study the dynamic meanvariance portfolio selection problem under which the stock price follows a CEV model, a Heston stochastic variance model and a jumpdiffusion risk model, respectively. By invoking the use of the stochastic linearquadratic approach, we obtain the closedform solutions of the efficient portfolio strategy and the efficient frontier. Then we study the stochastic differential portfolio games between the insurance company and the market in a jumpdiffusion model, and study the zerosum stochastic differential games problem in a Vasicek stochastic interest rate model. By using the linearquadratic method, we obtain the closedform soultions of the optimal portfolio strategy, the optimal market strategy and the optimal value function. Finally, we study the Robust utility maximization portfolio selection problem under which the stock price followed a CEV model. We also obtain the closedform solutions of the optimal portfolio strategy, the optimal equivalent probability scenario and the optimal value function using the linearquadratic technique.  Keywords/Search Tags:  CEV model, Heston stochastic volatility model, jumpdiffusion risk model, Vasicek stochastic interest model, inearquadratic, meanvariance, portfolio, efficient frontier, stochastic differential games, Robust utility maximization  PDF Full Text Request  Related items 
 
