Convex Duality for Epstein-Zin Stochastic Differential Utility
25 Pages Posted: 15 Jan 2016 Last revised: 2 Nov 2016
Date Written: January 14, 2016
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
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