Research Of The Hedging Problems Based On Stochastic Differential Game

Hedging is one of the hot topics of mathematical finance,and it is also a concern for hedgers.As financial markets become more and more unstable,investors want to get high profits at the same time want to take the minimum risk,so hedging has become a very good hedging tool.This is the main problem to be studied in this paper.The reality of the financial market will be affected by major events,important market factors level(such as the economic crisis,the financial storm,etc.),makes the stock price will appear discontinuous jumping.Therefore,the research contents of this paper are as follows:(1)Study hedging problem with stochastic volatility.When the stock price follows jump-diffusion process and Random fluctuations follows It? process,Application of stochastic differential game theory and HJBI equation,Studied the robust dynamic hedging problem with stochastic volatility.To get the optimal decision of hedging according to expression.(2)Study the Hedging problem under different utility functions.When the stock price follows jump-diffusion process,establishing the mathematical model of hedging,using It?formula,In two different utility function with the functional variational method,At last,the optimal decision expression of hedging is obtained under the respective utility function.(3)Research part information under the optimal hedging strategy with jump of the stock price.When the stock price follows jump-diffusion process,the securities parameterized random revenue,And establish the relevant hedging model,using Calman filtering technique,the problem of partial information is transformed into the problem of complete information.Using It? formula,the optimal hedging strategy is obtained.