The Annals of Applied Probability

Convex Duality in Constrained Portfolio Optimization

Jaksa Cvitanic and Ioannis Karatzas

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Abstract

We study the stochastic control problem of maximizing expected utility from terminal wealth and/or consumption, when the portfolio is constrained to take values in a given closed, convex subset of $\mathscr{R}^d$. The setting is that of a continuous-time, Ito process model for the underlying asset prices. General existence results are established for optimal portfolio/consumption strategies, by suitably embedding the constrained problem in an appropriate family of unconstrained ones, and finding a member of this family for which the corresponding optimal policy obeys the constraints. Equivalent conditions for optimality are obtained, and explicit solutions leading to feedback formulae are derived for special utility functions and for deterministic coefficients. Results on incomplete markets, on short-selling constraints and on different interest rates for borrowing and lending are covered as special cases. The mathematical tools are those of continuous-time martingales, convex analysis and duality theory.

Article information

Source
Ann. Appl. Probab., Volume 2, Number 4 (1992), 767-818.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005576

Digital Object Identifier
doi:10.1214/aoap/1177005576

Mathematical Reviews number (MathSciNet)
MR1189418

Zentralblatt MATH identifier
0770.90002

JSTOR
links.jstor.org

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 90A09 60H30: Applications of stochastic analysis (to PDE, etc.) 60G44: Martingales with continuous parameter 90A16 49N15: Duality theory

Keywords
Constrained optimization convex analysis duality stochastic contro portofolio and consumption processes martingale representations

Citation

Cvitanic, Jaksa; Karatzas, Ioannis. Convex Duality in Constrained Portfolio Optimization. Ann. Appl. Probab. 2 (1992), no. 4, 767--818. doi:10.1214/aoap/1177005576. https://projecteuclid.org/euclid.aoap/1177005576


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