Optimal martingale measure maximizing the expected total utility of consumption with applications to derivative pricing

In this article we discuss the problem of selecting an optimal equivalent martingale measure for discrete-time incomplete financial markets under the criteria of maximizing the expected total utility of consumption. For a given utility function, we choose a class of equivalent martingale measures, corresponding to each of which we construct a random variable. We show that if one of these random variables is an admissible consumption process, then this consumption is optimal, and the martingale measure associated with this consumption process is also optimal. For a specific market model with hyperbolic absolute risk aversion (HARA) utility functions, we work out the optimal consumption and optimal martingale measure explicitly, and further use this optimal martingale measure to give the fair price for any derivative.