IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v60y2015i3p393-422.html
   My bibliography  Save this article

Dynamic choice with constant source-dependent relative risk aversion

Author

Listed:
  • Costis Skiadas

Abstract

An axiomatic characterization of recursive utility with source-dependent constant relative risk aversion (CRRA), constant elasticity of intertemporal substitution, constant rate of impatience and subjective beliefs is established. The utility form is a minimal extension of Epstein–Zin–Weil utility that allows the CRRA to depend on the source of risk, a dependence that admits an ambiguity aversion interpretation. Dual representations of the proposed recursive utility are discussed and shown to be useful in tackling the central planner problem and associated asset pricing applications. An appendix presents the continuous-time version of the utility form, which preserves the effect of ambiguity aversion under Brownian/Poisson uncertainty, despite its smoothness. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Costis Skiadas, 2015. "Dynamic choice with constant source-dependent relative risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 393-422, November.
    • Handle: RePEc:spr:joecth:v:60:y:2015:i:3:p:393-422
    DOI: 10.1007/s00199-015-0920-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-015-0920-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-015-0920-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kenneth A. Froot, 1999. "Introduction to "The Financing of Catastrophe Risk"," NBER Chapters, in: The Financing of Catastrophe Risk, pages 1-22, National Bureau of Economic Research, Inc.
    2. Mark Schroder & Costis Skiadas, 2008. "Optimality And State Pricing In Constrained Financial Markets With Recursive Utility Under Continuous And Discontinuous Information," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 199-238, April.
    3. Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, vol. 49(8), pages 1089-1104, August.
    4. Kenneth A. Froot, 1999. "The Financing of Catastrophe Risk," NBER Books, National Bureau of Economic Research, Inc, number froo99-1, March.
    5. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    6. Froot, Kenneth A. (ed.), 1999. "The Financing of Catastrophe Risk," National Bureau of Economic Research Books, University of Chicago Press, number 9780226266237, December.
    7. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    8. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    9. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    11. Darrell Duffie, 2010. "Presidential Address: Asset Price Dynamics with Slow‐Moving Capital," Journal of Finance, American Finance Association, vol. 65(4), pages 1237-1267, August.
    12. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    13. Dumas, Bernard & Uppal, Raman & Wang, Tan, 2000. "Efficient Intertemporal Allocations with Recursive Utility," Journal of Economic Theory, Elsevier, vol. 93(2), pages 240-259, August.
    14. 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.
    15. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    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. Łukasz Balbus, 2020. "On recursive utilities with non-affine aggregator and conditional certainty equivalent," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 551-577, September.
    2. Zheng Li & Jingjing Zeng, 2023. "Increasing relative risk taking in a choice context with source-dependent travel time risks," Transportation, Springer, vol. 50(6), pages 2441-2460, December.
    3. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.

    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. Yu Chen & Thomas Cosimano & Alex Himonas & Peter Kelly, 2014. "An Analytic Approach for Stochastic Differential Utility for Endowment and Production Economies," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 397-443, December.
    2. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    3. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    4. Wei, Pengyu & Yang, Charles & Zhuang, Yi, 2023. "Robust consumption and portfolio choice with derivatives trading," European Journal of Operational Research, Elsevier, vol. 304(2), pages 832-850.
    5. Dejian Tian & Weidong Tian, 2016. "Comparative statics under κ-ambiguity for log-Brownian asset prices," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 361-378, December.
    6. Jeong, Daehee & Kim, Hwagyun & Park, Joon Y., 2015. "Does ambiguity matter? Estimating asset pricing models with a multiple-priors recursive utility," Journal of Financial Economics, Elsevier, vol. 115(2), pages 361-382.
    7. Suzuki, Masataka, 2018. "Continuous-time smooth ambiguity preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 30-44.
    8. Zhu, Wenge, 2017. "Wanting robustness in insurance: A model of catastrophe risk pricing and its empirical test," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 14-23.
    9. Roche, Hervé, 2011. "Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 80-96, January.
    10. 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.
    11. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    12. 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.
    13. Julian Thimme, 2017. "Intertemporal Substitution In Consumption: A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 226-257, February.
    14. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    15. Christian Traeger, 2014. "Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 627-664, August.
    16. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    17. 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.
    18. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    19. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
    20. Max Gillman & Michal Kejak & Michal Pakoš, 2015. "Learning about Rare Disasters: Implications For Consumption and Asset Prices," Review of Finance, European Finance Association, vol. 19(3), pages 1053-1104.

    More about this item

    Keywords

    Source-dependent risk aversion; Ambiguity aversion ; Recursive utility; Epstein–Zin–Weil utility; Small-risk approximations; D81; D91; G12;
    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:spr:joecth:v:60:y:2015:i:3:p:393-422. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.