Convex Duality for Epstein-Zin Stochastic Differential Utility

25 Pages Posted: 15 Jan 2016 Last revised: 2 Nov 2016

See all articles by Anis Matoussi

Anis Matoussi

Ecole Polytechnique, Paris

Hao Xing

Boston University - Questrom School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: January 14, 2016

Abstract

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and Epstein-Zin stochastic differential utility. Duality between the primal and dual problems is established. Consequently the optimal strategy of this consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.

Keywords: Consumption investment optimization, Convex duality, Stochastic differential utility, Backward stochastic differential equation

JEL Classification: G11, D91

Suggested Citation

Matoussi, Anis and Xing, Hao, Convex Duality for Epstein-Zin Stochastic Differential Utility (January 14, 2016). Available at SSRN: https://ssrn.com/abstract=2715425 or http://dx.doi.org/10.2139/ssrn.2715425

Anis Matoussi

Ecole Polytechnique, Paris

1 rue Descartes
Paris, 75005
France

Hao Xing (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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