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Consumption–investment optimization with Epstein–Zin utility in incomplete markets

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  • Hao Xing

    (London School of Economics and Political Science)

Abstract

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.

Suggested Citation

  • Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:1:d:10.1007_s00780-016-0297-z
    DOI: 10.1007/s00780-016-0297-z
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    Citations

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    Cited by:

    1. Joshua Aurand & Yu-Jui Huang, 2020. "Mortality and Healthcare: a Stochastic Control Analysis under Epstein-Zin Preferences," Papers 2003.01783, arXiv.org, revised Jul 2021.
    2. Joshua Aurand & Yu-Jui Huang, 2019. "Epstein-Zin Utility Maximization on a Random Horizon," Papers 1903.08782, arXiv.org, revised May 2023.
    3. Campani, Carlos Heitor & Garcia, René, 2019. "Approximate analytical solutions for consumption/investment problems under recursive utility and finite horizon," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 364-384.
    4. Dariusz Zawisza, 2020. "On the parabolic equation for portfolio problems," Papers 2003.13317, arXiv.org, revised Oct 2020.
    5. 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.
    6. 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.
    7. Shigeta, Yuki, 2020. "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    8. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
    9. Rodwell Kufakunesu & Calisto Guambe & Lesedi Mabitsela, 2018. "Risk-based optimal portfolio of an insurer with regime switching and noisy memory," Papers 1808.04604, arXiv.org, revised Mar 2019.
    10. Zhao, Hui & Wang, Suxin, 2022. "Optimal investment and benefit adjustment problem for a target benefit pension plan with Cobb-Douglas utility and Epstein-Zin recursive utility," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1166-1180.
    11. 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.
    12. Chen, Xingjiang & Ruan, Xinfeng & Zhang, Wenjun, 2021. "Dynamic portfolio choice and information trading with recursive utility," Economic Modelling, Elsevier, vol. 98(C), pages 154-167.
    13. 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.
    14. Immacolata Oliva & Ilaria Stefani, 2023. "Co-jumps and recursive preferences in portfolio choices," Annals of Finance, Springer, vol. 19(3), pages 291-324, September.
    15. Martin Herdegen & David Hobson & Alex S. L. Tse, 2024. "Portfolio Optimization under Transaction Costs with Recursive Preferences," Papers 2402.08387, arXiv.org.
    16. 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.
    17. Yaroslav Melnyk & Johannes Muhle‐Karbe & Frank Thomas Seifried, 2020. "Lifetime investment and consumption with recursive preferences and small transaction costs," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1135-1167, July.
    18. Kraft, Holger & Munk, Claus & Weiss, Farina, 2022. "Bequest motives in consumption-portfolio decisions with recursive utility," Journal of Banking & Finance, Elsevier, vol. 138(C).
    19. John Armstrong & Cristin Buescu, 2020. "Asymptotically Optimal Management of Heterogeneous Collectivised Investment Funds," Papers 2004.01506, arXiv.org.
    20. Marcelo Lewin & Carlos Heitor Campani, 2023. "Constrained portfolio strategies in a regime-switching economy," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 27-59, March.
    21. Matoussi, Anis & Xing, Hao, 2018. "Convex duality for Epstein-Zin stochastic differential utility," LSE Research Online Documents on Economics 82519, London School of Economics and Political Science, LSE Library.
    22. Campani, Carlos Heitor & Garcia, René & Lewin, Marcelo, 2021. "Optimal portfolio strategies in the presence of regimes in asset returns," Journal of Banking & Finance, Elsevier, vol. 123(C).

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    More about this item

    Keywords

    Consumption–investment optimization; Epstein–Zin utility; Backward stochastic differential equation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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