IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpfi/0503021.html

On the viscosity solutions of a stochastic differential utility problem

Author

Listed:
  • Fabio Antonelli
  • Andrea Pascucci

Abstract

We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for degenerate nonlinear partial differential equation. We also characterize the solution in the vanishing viscosity sense.

Suggested Citation

  • Fabio Antonelli & Andrea Pascucci, 2005. "On the viscosity solutions of a stochastic differential utility problem," Finance 0503021, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0503021
    Note: Type of Document - pdf; pages: 19
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0503/0503021.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, University Library of Munich, Germany.
    2. Guangbao Guo, 2018. "Finite Difference Methods for the BSDEs in Finance," IJFS, MDPI, vol. 6(1), pages 1-15, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kohlmann, Michael, 1999. "(Reflected) Backward Stochastic Differential Equations and Contingent Claims," CoFE Discussion Papers 99/10, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. 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.
    3. Dominika Czyz & Karolina Safarzynska, 2023. "Catastrophic Damages and the Optimal Carbon Tax Under Loss Aversion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 85(2), pages 303-340, June.
    4. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.
    5. Chabakauri, Georgy, 2010. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 43142, London School of Economics and Political Science, LSE Library.
    6. Isaenko, Sergei, 2008. "The term structure of interest rates in a pure exchange economy where investors have heterogeneous recursive preferences," The Quarterly Review of Economics and Finance, Elsevier, vol. 48(3), pages 457-481, August.
    7. Roberto Marfè, 2015. "Labor Rigidity and the Dynamics of the Value Premium," Carlo Alberto Notebooks 429, Collegio Carlo Alberto.
    8. repec:pri:metric:wp033_2012_hansen_borovicka_hendricks_scheinkman_risk%20price%20dynamics. is not listed on IDEAS
    9. Min Dai & Yuchao Dong & Yanwei Jia & Xun Yu Zhou, 2026. "Merton's Problem with Recursive Perturbed Utility," Papers 2602.13544, arXiv.org.
    10. Ma, Chenghu, 1998. "Attitudes toward the timing of resolution of uncertainty and the existence of recursive utility," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 97-112, September.
    11. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    12. Frederick Ploeg, 2021. "Carbon pricing under uncertainty," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 28(5), pages 1122-1142, October.
    13. Shi, Huihong & Mu, Congming & Yang, Jinqiang & Huang, Wenli, 2021. "A Sino-US comparative analysis of the hi-tech entrepreneurial model," Economic Modelling, Elsevier, vol. 94(C), pages 953-966.
    14. Gopalakrishna, Goutham & Lee, Seung Joo & Papamichalis, Theofanis, 2025. "Beliefs and the net worth trap," Journal of Economic Theory, Elsevier, vol. 227(C).
    15. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    16. Camelia Minoiu & Andrés Schneider & Min Wei, 2023. "Term Premium and Bank Lending," Finance and Economics Discussion Series 2023-049r1, Board of Governors of the Federal Reserve System (U.S.), revised 06 Jul 2026.
    17. 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.
    18. Dejian Tian & Weidong Tian & Jianjun Zhou & Zimu Zhu, 2025. "Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint," Papers 2509.21929, arXiv.org, revised Oct 2025.
    19. Knut K. Aase, 2016. "Recursive utility using the stochastic maximum principle," Quantitative Economics, Econometric Society, vol. 7(3), pages 859-887, November.
    20. Olivier Menoukeu Pamen, 2017. "Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 373-410, November.
    21. Junchi Ma & Mobolaji Ogunsolu & Jinniao Qiu & Ayşe Deniz Sezer, 2023. "Credit risk pricing in a consumption‐based equilibrium framework with incomplete accounting information," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 666-708, July.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • G - Financial Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0503021. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA The email address of this maintainer does not seem to be valid anymore. Please ask EconWPA to update the entry or send us the correct address (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.