The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the...

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity...

We give a review of classical and recent results on maximization of expected utility for an investor who has the possibility of trading in a financial market. Emphasis will be given to the duality theory related to this convex optimization problem.(...)