The Annals of Applied Probability

Dual Formulation of the Utility Maximization Problem Under Transaction Costs

Griselda Deelstra, Huyên Pham, and Nizar Touzi

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Abstract

In the context of a general multivariate financial market with transaction costs, we consider the problem of maximizing expected utility from terminal wealth. In contrast with the existing literature, where only the liquidation value of the terminal portfolio is relevant, we consider general utility functions which are only required to be consistent with the structure of the transaction costs. An important feature of our analysis is that the utility function is not required to be $C^1$. Such nonsmoothness is suggested by major natural examples. Our main result is an extension of the well-known dual formulation of the utility maximization problem to this context.

Article information

Source
Ann. Appl. Probab., Volume 11, Number 4 (2001), 1353-1383.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015345406

Digital Object Identifier
doi:10.1214/aoap/1015345406

Mathematical Reviews number (MathSciNet)
MR1878301

Zentralblatt MATH identifier
1012.60059

Subjects
Primary: 90A09 93E20: Optimal stochastic control 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 90A16

Keywords
Utility maximization transaction costs dual formulation nonsmooth analysis

Citation

Deelstra, Griselda; Pham, Huyên; Touzi, Nizar. Dual Formulation of the Utility Maximization Problem Under Transaction Costs. Ann. Appl. Probab. 11 (2001), no. 4, 1353--1383. doi:10.1214/aoap/1015345406. https://projecteuclid.org/euclid.aoap/1015345406


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  • ENSAE, Timbre J120 15 Boulevard Gabriel P´eri 92245 Malakoff Cedex France E-mail: deelstra@ensae.fr H. Pham Laboratoire de Probabilit´es et Mod eles Al´eatoires CNRS UMR 7599 Universit´e Paris 7 France E-mail: pham@gauss.math.jussieu.fr N. Touzi Centre de Recherche en Economie et Statistique 15 Boulevard Gabriel P´eri 92245 Malakoff Cedex France E-mail: touzi@ensae.fr