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Stochastic differential utility as the continuous-time limit of recursive utility

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  • Kraft, Holger
  • Seifried, Frank Thomas

Abstract

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus [21], converges to stochastic differential utility, as introduced by Duffie and Epstein [10], in the continuous-time limit of vanishing grid size.

Suggested Citation

  • Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:528-550
    DOI: 10.1016/j.jet.2013.12.007
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    2. Suzuki, Masataka, 2018. "Continuous-time smooth ambiguity preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 30-44.
    3. Augeraud-Véron, Emmanuelle & Fabbri, Giorgio & Schubert, Katheline, 2021. "Volatility-reducing biodiversity conservation under strategic interactions," Ecological Economics, Elsevier, vol. 190(C).
    4. 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.
    5. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    6. Fahrenwaldt, Matthias Albrecht & Jensen, Ninna Reitzel & Steffensen, Mogens, 2020. "Nonrecursive separation of risk and time preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 95-108.
    7. Oliver de Groot & Alexander W. Richter & Nathaniel A. Throckmorton, 2022. "Valuation risk revalued," Quantitative Economics, Econometric Society, vol. 13(2), pages 723-759, May.
    8. Shigeta, Yuki, 2020. "Gain/loss asymmetric stochastic differential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 118(C).
    9. Kraft, Holger & Weiss, Farina, 2019. "Consumption-portfolio choice with preferences for cash," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 40-59.
    10. Christian Bender & Christian Gärtner & Nikolaus Schweizer, 2018. "Pathwise Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 965-965, August.
    11. 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.
    12. Johnson Kakeu, 2023. "Concerns for Long-Run Risks and Natural Resource Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 84(4), pages 1051-1093, April.
    13. 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.
    14. David Hobson & Martin Herdegen & Joseph Jerome, 2021. "The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility," Papers 2107.06593, arXiv.org.
    15. Shigeta, Yuki, 2022. "Quasi-hyperbolic discounting under recursive utility and consumption–investment decisions," Journal of Economic Theory, Elsevier, vol. 204(C).
    16. Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.
    17. Chabakauri, Georgy, 2015. "Dynamic equilibrium with rare events and heterogeneous Epstein-Zin investors," LSE Research Online Documents on Economics 60737, London School of Economics and Political Science, LSE Library.
    18. Gareth Lui-Evans & Shalini Mitra, 2019. "Informality and Bank Stability," Working Papers 201903, University of Liverpool, Department of Economics.
    19. Martin Herdegen & David Hobson & Joseph Jerome, 2021. "Proper solutions for Epstein-Zin Stochastic Differential Utility," Papers 2112.06708, arXiv.org.
    20. Kraft, Holger & Munk, Claus & Weiss, Farina, 2022. "Bequest motives in consumption-portfolio decisions with recursive utility," Journal of Banking & Finance, Elsevier, vol. 138(C).
    21. Chabakauri, Georgy, 2015. "Dynamic equilibrium with rare events and heterogeneous epstein-zin investors," LSE Research Online Documents on Economics 62003, London School of Economics and Political Science, LSE Library.
    22. 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.

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    More about this item

    Keywords

    Stochastic differential utility; Recursive utility; Convergence; Backward stochastic differential equation;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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