Convex Duality for Epstein–Zin Stochastic Differential Utility

29 Pages Posted: 17 Sep 2018

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: October 2018

Abstract

This paper introduces a dual problem to study a continuous‐time consumption and investment problem with incomplete markets and Epstein–Zin stochastic differential utilities. 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 models, utility specifications, and agent's admissible strategies. 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: backward stochastic differential equation, consumption investment optimization, convex duality, stochastic differential utility

Suggested Citation

Matoussi, Anis and Xing, Hao, Convex Duality for Epstein–Zin Stochastic Differential Utility (October 2018). Mathematical Finance, Vol. 28, Issue 4, pp. 991-1019, 2018, Available at SSRN: https://ssrn.com/abstract=3248623 or http://dx.doi.org/10.1111/mafi.12168

Anis Matoussi (Contact Author)

Ecole Polytechnique, Paris

1 rue Descartes
Paris, 75005
France

Hao Xing

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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