On optimal terminal wealth under transaction costs

In this note, we show that the modern approach to the problem of maximizing expected utility from terminal wealth in financial markets, namely marting ale/duality methodology, works also in the presence of proportional transac tion costs. More precisely, we show that the optimal terminal wealth is giv en as the inverse of marginal utility evaluated at the random variable whic h is optimal for an appropriately defined dual problem. We thereby resolve a question left open by [Mathematical Finance 6 (1996) 133]. (C) 2001 Elsev ier Science B.V. All rights reserved.