Based on some non-attainable contingent claims which present prices are known in the incomplete markets, the paper provides more investment opportunities to the investers, then modifies the expression of martingale representation theorem,so that the inner risk is reduced.

A Study of Asset Price in the Incomplete Financial Markets;

Continuous-time hedging under complete market by BSDEs;

In a complete market, resources location is Pareto efficient, and risk can be shared and offset.

Financial mathematical knowledge such as partial differential equation,Brownian motion,hedge,risk-neutral probability,option pricing under complete market and so on is necessaryly needed.

Modeling for Pricing Futures in Incomplete Markets;

Arbitrage and equilibrium of smooth infinite incomplete markets;

This paper presumed that the market is an imperfect market,and then by considering the factors of the difference of capital cost and information,it discussed the impact of assets price of heterogeneity investors under uncertain conditions.