Research Of The Hedging Questions Based On The Mean-Variance

Hedging problem has been developed into one of the hot problems of mathematical finance,and also been concerned by investors.As the financial crisis broke out,the financial markets become more volatile,investors want to get higher profits at the same time want to minimal risk,so the hedging has become a good tool.Because many factors would bring some changes to the financial markets,the stock price is discontinuous jumps.So based on the mean-variance criterion,the problem of hedging is studied mainly in this paper when the stock price follows three different process with a mixed of contingent claim.(1)The hedging of mixed contingent claim is studied when the stock price follows the jump-diffusion process and the stochastic cash flow.Based on the mean-variance criterion,a hedging model of mixed contingent claim is established when the stock price subjects to the jump-diffusion process and the stochastic cash flow.First discussed two mixed contingent claim,which has been generalized to n.By using backward stochastic differential equation(Hereinafter referred to as BSDE),It? formula,and stochastic LQ control method,finding the optimal hedging strategy,then the relationship is discussed between the mixed contingent Claim and the individual contingent claim.(2)The hedging of mixed contingent claim is studied under the partial information when the stock price follows the jump-diffusion process.The financial markets will be influenced by some factors,the risk of asset price will jump,then considering the model of the risk of asset price subjects to the jump-diffusion process,at the same time the securities market will be affected by other factors,making the random yields of risky asset is sparameterized and follows a It? process,then establishing the hedging model of mixed contingent claim under partial information when the stock price follows jump-diffusion,the partial information is transformed into the complete information by using the filter technology.By using backward stochastic differential equation,formula,and the stochastic LQ control method,finding the optimal hedging strategy at the same time discusses the relationship between two mixed contingent claim and the individual contingent claim.(3)The hedging of mixed contingent claim is studied when the stock price follows the Lévy process.The stock price follows Lévy process and is affected by the Markovmotion when the stock price is hit greatly,based on the mean-variance criterion,the hedging model is established.By using backward stochastic differential equation,formula,and the stochastic LQ control method finding the optimal hedging strategy with two and n mixture of contingent claim,then the relationship is discussed between the mixed contingent claim and the individual contingent claim.