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November, 1992 Convex Duality in Constrained Portfolio Optimization
Jaksa Cvitanic, Ioannis Karatzas
Ann. Appl. Probab. 2(4): 767-818 (November, 1992). DOI: 10.1214/aoap/1177005576


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.


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Jaksa Cvitanic. Ioannis Karatzas. "Convex Duality in Constrained Portfolio Optimization." Ann. Appl. Probab. 2 (4) 767 - 818, November, 1992.


Published: November, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0770.90002
MathSciNet: MR1189418
Digital Object Identifier: 10.1214/aoap/1177005576

Primary: 93E20
Secondary: 49N15 , 60G44 , 60H30 , 90A09 , 90A16

Keywords: constrained optimization , convex analysis , Duality , martingale representations , portofolio and consumption processes , stochastic contro

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.2 • No. 4 • November, 1992
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