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Convex duality for Epstein–Zin 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 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.

Suggested Citation

  • Anis Matoussi & Hao Xing, 2018. "Convex duality for Epstein–Zin stochastic differential utility," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 991-1019, October.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:4:p:991-1019
    DOI: 10.1111/mafi.12168
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    Citations

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    Cited by:

    1. Martin Herdegen & David Hobson & Joseph Jerome, 2023. "The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. II: Existence, uniqueness and verification for ϑ ∈ ( 0 , 1 ) $\vartheta \in (0,1)$," Finance and Stochastics, Springer, vol. 27(1), pages 159-188, January.
    2. Michael Monoyios & Oleksii Mostovyi, 2022. "Stability of the Epstein-Zin problem," Papers 2208.09895, arXiv.org, revised Apr 2023.
    3. Li, Hanwu & Riedel, Frank & Yang, Shuzhen, 2024. "Optimal consumption for recursive preferences with local substitution — the case of certainty," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    4. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    5. Zixin Feng & Dejian Tian, 2021. "Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints," Papers 2111.09032, arXiv.org, revised May 2023.
    6. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    7. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    8. Martin Herdegen & David Hobson & Joseph Jerome, 2023. "The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations," Finance and Stochastics, Springer, vol. 27(1), pages 127-158, January.
    9. David Hobson & Martin Herdegen & Joseph Jerome, 2021. "The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility," Papers 2107.06593, arXiv.org.
    10. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Optimal consumption-investment with coupled constraints on consumption and investment strategies in a regime switching market with random coefficients," Papers 2211.05291, arXiv.org.
    11. Zixin Feng & Dejian Tian & Harry Zheng, 2024. "Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets," Papers 2407.19995, arXiv.org.
    12. Martin Herdegen & David Hobson & Joseph Jerome, 2021. "Proper solutions for Epstein-Zin Stochastic Differential Utility," Papers 2112.06708, arXiv.org.
    13. Kexin Chen & Kyunghyun Park & Hoi Ying Wong, 2024. "Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences," Papers 2406.12305, arXiv.org.

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