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 martingale/duality methodology, works also in the presence of proportional transaction costs. More precisely, we show that the optimal terminal wealth is given as the inverse of marginal utility evaluated at the random variable which is optimal for an appropriately defined dual problem. We thereby resolve a question left open by [Mathematical Finance 6 (1996) 133]. (C) 2001 Elsevier Science B.V. All rights reserved.