Martingale Measure Method for Expected Utility
Maximization in Discrete-Time Incomplete Markets

Ping Li

Jianming Xia
and  Jia-an Yan

In this paper we study the expected utility maximization problem for discrete-time incomplete financial markets. As shown by Xia and Yan (2000a, 2000b) in the continuous-time case, this problem can be solved by the martingale measure method. In a special discrete-time model, we explicitly work out the optimal trading strategies and the associated minimum relative entropy martingale measures and minimum Hellinger-Kakutani distance martingale measures.

Key Words: Martingale measure; Incomplete market; Utility maximization; Optimal trading strategy; Relative entropy; Hellinger-Kakutani distance.
JEL Classification Numbers: G11, G13.