In this paper,we study the minimal entropy martingale measure of Brown motion with jump.

Using the dynamic programming approach,the minimal entropy martingale measure is constructed by the utility indifference pricing,the minimal martingale measure and the variance-optimal martingale measures are given.

The explicit expressions of some special equivalent martingale measure are given,such as the minimal entropy martingale measure,the minimal reverse relative entropy martingale measure,the variance-optimal martingale measure and the minimal martingale measure.

An European option pricing formula was gained by methods of equivalent martingale measure.

The Gisanov theorem is applied to constructing the equivalent martingale measure and the Ito formula,and using of the reflection principle helps simplifying the pricing formula.

Based on the Black-Scholes option pricing theory, the equivalent martingale measure is constructed to obtain the optimal strategy of an optimal investment problem.

Under the framework of equivalent martingale measures,we discuss the pricing formulas of power payoffs European options with continuous dividend at the time of maturity of the options.

Under stochastic interest, by using of equivalent martingale measures model, we discuss single - factor model and two-factor model respectively, and obtain pricing formula of European option on foreign currency.

All equivalent martingale measures and the minimal reverse entropy martingale measure in a diffusion model are obtained.

We give the minimal martingale measure under this model and consider the hedging problem of the unit-linked life insurance contract under local risk minimization.

The exact expressions of minimal martingale measure and the minimal entropy martingale measure for jump diffusion semimartingale are gained,with the specific changes of intensity and density function processes in these measures.