Application of Relative Entropy in Finding the Minimal Equivalent Martingale Measure

Minimal entropy martingale measure (MEMM) and geometric Levy process has been introduced as a pricing model for the incomplete financial market. This model has many good properties and is applicable to very wide classes of underlying asset price processes. MEMM is the nearest equivalent martingale measure to the original probability in the sense of Kullback-Leibler distance and is closely related to the large deviation theory .Those good properties has been explained. MEMM is also justified for option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion and Markov-modulated exponential Levy model.