Optimal Strategies for Utility from Terminal Wealth with General Bid and Ask Prices

In the paper we study utility from terminal wealth maximization with general bid and ask prices studying first one asset case and generalizing then results to the multi asset case. We show that under certain assumptions (continuous conditional distribution of the assets) and strict concavity of the utility function the problem can be reduced to study a static problem and then by an induction to consider multi period case. We obtain formulae for buying, selling and no transaction zones both in one and two asset cases. We also show the existence and the form of shadow prices.