The Application On Optimal Investment Strategy By Martingale

Since the initiation of continuous-time portfolio selection theory (Merton 1969&1971),many new financial concepts have been used to describe investor'problems. Dynamic programming approach relies heavily upon the standard me-thods,and finally the portfolio optimization problem comes to solving a second-order nonlinear partial differential equation. By using the theory of martingale approach and statistical analysis,this paper studies the above question. Firstly,from the microstructure of market and combining the base frame of finance economic analysis,we discuss the problem of consumer and optimal portfolio with analysis method of martingale. By carrying out research about the optimal answer,while there is no restriction on portfolio,we get a consump-tion process and an investment strategy. Secondly,for researching the above problem,we have constructed a self-contained auxiliary market and carried out some reasoning with the theory of martingale. We get a numerical explanation and construct a general analysis frame on portfolio and study the market with or without risk and the common meaning market. As a result,we compared the three markets on avail relation. Finally,we studied portfolio problems with hazard constraint using twice maximization model. We give out a group of optimal policy values under speci-fic market parameter values and their economic explanations.