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A generalized stochastic differential utility

Author

Listed:
  • Ali Lazrak

    (Sauder - Sauder School of Business [British Columbia] - UBC - University of British Columbia)

  • Marie-Claire Quenez

    (LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper generalizes, in the setting of Brownian information, the Duffie-Epstein (1992) stochastic differential formulation of intertemporal recursive utility (SDU). We provide a utility functional of state-contingent consumption plans that exhibits a local dependency with respect to the utility intensity process (the integrand of the quadratic variation) and call it the generalized SDU. This mathematical generalization of the SDU permits, in fact, more flexibility in the separation between risk aversion and intertemporal substitution and allows to model asymmetry in risk aversion.We extensively use the backward stochastic differential equation theory to give sufficient conditions for comparative and absolute risk aversion behavior as well as aversion to specific directional risk. Additionally, we discuss whether our functional exhibits monotonicity to its information filtration argument. For purposes of illustration, we provide some applications to the consumption/portfolio strategy selection problem in a complete securities market.

Suggested Citation

  • Ali Lazrak & Marie-Claire Quenez, 2003. "A generalized stochastic differential utility," Post-Print hal-00485718, HAL.
    • Handle: RePEc:hal:journl:hal-00485718
    DOI: 10.1287/moor.28.1.154.14259
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    Citations

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    Cited by:

    1. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    2. Augeraud-Véron, Emmanuelle & Fabbri, Giorgio & Schubert, Katheline, 2021. "Volatility-reducing biodiversity conservation under strategic interactions," Ecological Economics, Elsevier, vol. 190(C).
    3. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
    4. Ali Lazrak, 2005. "Generalized stochastic differential utility and preference for information," Papers math/0503579, arXiv.org.
    5. Sigrid Källblad, 2017. "Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals," Finance and Stochastics, Springer, vol. 21(2), pages 397-425, April.
    6. Jaime A. Londo~no, 2006. "State Dependent Utility," Papers math/0603316, arXiv.org.
    7. Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
    8. Patrick Beissner & Qian Lin & Frank Riedel, 2020. "Dynamically consistent alpha‐maxmin expected utility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1073-1102, July.
    9. Lazrak, Ali & Zapatero, Fernando, 2004. "Efficient consumption set under recursive utility and unknown beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 207-226, February.
    10. Dejian Tian, 2022. "Pricing principle via Tsallis relative entropy in incomplete market," Papers 2201.05316, arXiv.org, revised Oct 2022.
    11. Nobuhiro Nakamura, 2004. "Numerical Approach to Asset Pricing Models with Stochastic Differential Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 267-300, September.
    12. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    13. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    14. Roger J. A. Laeven & Emanuela Rosazza Gianin & Marco Zullino, 2023. "Dynamic Return and Star-Shaped Risk Measures via BSDEs," Papers 2307.03447, arXiv.org, revised Jul 2023.

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