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Convex duality for Epstein–Zin stochastic differential utility
Authors:Anis Matoussi  Hao Xing
Affiliation:1. Université du Maine, Le Mans, and CMAP, Ecole Polytechnique, France;2. Department of Statistics, London School of Economics and Political Science, London, UK
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
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