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Convex duality for stochastic differential utility

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  • Anis Matoussi
  • Hao Xing

Abstract

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the 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.

Suggested Citation

  • Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.
    • Handle: RePEc:arx:papers:1601.03562
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    References listed on IDEAS

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    Cited by:

    1. Shaolin Ji & Xiaomin Shi, 2016. "Recursive utility optimization with concave coefficients," Papers 1607.00721, arXiv.org.

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