IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v75y2023i3d10.1007_s00199-022-01428-2.html
   My bibliography  Save this article

Cautious stochastic choice, optimal stopping and deliberate randomization

Author

Listed:
  • Vicky Henderson

    (University of Warwick)

  • David Hobson

    (University of Warwick)

  • Matthew Zeng

    (University of Warwick)

Abstract

We study cautious stochastic choice (CSC) agents facing optimal timing decisions in a dynamic setting. In an expected utility setting, the optimal strategy is always a threshold strategy—to stop/sell the first time the price process exits an interval. In contrast, we show that in the CSC setting, where the agent has a family of utility functions and is concerned with the worst case certainty equivalent, the optimal strategy may be of non-threshold form and may involve randomization. We provide some carefully constructed examples, including one where we can solve explicitly for the optimal stopping rule and show it is a non-trivial mixture of threshold strategies. Our model is consistent with recent experimental evidence in dynamic setups whereby individuals do not play cut-off or threshold strategies.

Suggested Citation

  • Vicky Henderson & David Hobson & Matthew Zeng, 2023. "Cautious stochastic choice, optimal stopping and deliberate randomization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 887-922, April.
    • Handle: RePEc:spr:joecth:v:75:y:2023:i:3:d:10.1007_s00199-022-01428-2
    DOI: 10.1007/s00199-022-01428-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-022-01428-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-022-01428-2?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. Drew Fudenberg & Philipp Strack & Tomasz Strzalecki, 2018. "Speed, Accuracy, and the Optimal Timing of Choices," American Economic Review, American Economic Association, vol. 108(12), pages 3651-3684, December.
    2. Ryan Oprea & Daniel Friedman & Steven T. Anderson, 2009. "Learning to Wait: A Laboratory Investigation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1103-1124.
    3. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
    6. J. J. McCall, 1970. "Economics of Information and Job Search," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(1), pages 113-126.
    7. George J. Stigler, 1962. "Information in the Labor Market," NBER Chapters, in: Investment in Human Beings, pages 94-105, National Bureau of Economic Research, Inc.
    8. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    10. Urs Fischbacher & Gerson Hoffmann & Simeon Schudy, 2017. "The Causal Effect of Stop-Loss and Take-Gain Orders on the Disposition Effect," Review of Financial Studies, Society for Financial Studies, vol. 30(6), pages 2110-2129.
    11. Philipp Strack & Paul Viefers, 2021. "Too Proud to Stop: Regret in Dynamic Decisions," Journal of the European Economic Association, European Economic Association, vol. 19(1), pages 165-199.
    12. Terrance Odean, 1998. "Are Investors Reluctant to Realize Their Losses?," Journal of Finance, American Finance Association, vol. 53(5), pages 1775-1798, October.
    13. Kyle, Albert S. & Ou-Yang, Hui & Xiong, Wei, 2006. "Prospect theory and liquidation decisions," Journal of Economic Theory, Elsevier, vol. 129(1), pages 273-288, July.
    14. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    15. Fabio Maccheroni, 2002. "Maxmin under risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 823-831.
    16. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    17. Karni, Edi & Safra, Zvi, 1990. "Behaviorally consistent optimal stopping rules," Journal of Economic Theory, Elsevier, vol. 51(2), pages 391-402, August.
    18. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    19. Jonathan E. Ingersoll & Lawrence J. Jin, 2013. "Realization Utility with Reference-Dependent Preferences," Review of Financial Studies, Society for Financial Studies, vol. 26(3), pages 723-767.
    20. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    21. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    22. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
    23. Vicky Henderson, 2012. "Prospect Theory, Liquidation, and the Disposition Effect," Management Science, INFORMS, vol. 58(2), pages 445-460, February.
    24. Pedersen, J. L. & Peskir, G., 2001. "The Azéma-Yor embedding in non-singular diffusions," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 305-312, December.
    25. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    26. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2019. "Deliberately Stochastic," American Economic Review, American Economic Association, vol. 109(7), pages 2425-2445, July.
      • Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2012. "Deliberately Stochastic," PIER Working Paper Archive 17-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 May 2017.
    27. Yudistira Permana, 2020. "Why do people prefer randomisation? An experimental investigation," Theory and Decision, Springer, vol. 88(1), pages 73-96, February.
    28. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    29. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    30. Sebastian Ebert & Philipp Strack, 2015. "Until the Bitter End: On Prospect Theory in a Dynamic Context," American Economic Review, American Economic Association, vol. 105(4), pages 1618-1633, April.
    31. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.
    32. Grenadier, Steven R, 1996. "The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets," Journal of Finance, American Finance Association, vol. 51(5), pages 1653-1679, December.
    33. Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    Full references (including those not matched with items on IDEAS)

    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. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    2. Philipp Strack & Paul Viefers, 2021. "Too Proud to Stop: Regret in Dynamic Decisions," Journal of the European Economic Association, European Economic Association, vol. 19(1), pages 165-199.
    3. Henderson, Vicky & Hobson, David & Tse, Alex S.L., 2018. "Probability weighting, stop-loss and the disposition effect," Journal of Economic Theory, Elsevier, vol. 178(C), pages 360-397.
    4. Vicky Henderson & Jonathan Muscat, 2020. "Partial liquidation under reference-dependent preferences," Finance and Stochastics, Springer, vol. 24(2), pages 335-357, April.
    5. Chew, Soo Hong & Miao, Bin & Shen, Qiang & Zhong, Songfa, 2022. "Multiple-switching behavior in choice-list elicitation of risk preference," Journal of Economic Theory, Elsevier, vol. 204(C).
    6. Markus Dertwinkel-Kalt & Jonas Frey, 2020. "Optimal Stopping in a Dynamic Salience Model," CESifo Working Paper Series 8496, CESifo.
    7. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    8. Wei Ma, 2023. "Random dual expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 293-315, February.
    9. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2019. "Deliberately Stochastic," American Economic Review, American Economic Association, vol. 109(7), pages 2425-2445, July.
      • Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2012. "Deliberately Stochastic," PIER Working Paper Archive 17-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 May 2017.
    10. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    11. Guo, Liang, 2021. "Contextual deliberation and the choice-valuation preference reversal," Journal of Economic Theory, Elsevier, vol. 195(C).
    12. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning analysis of stock market anomalies under prospect stochastic dominance," Working Papers unige:134101, University of Geneva, Geneva School of Economics and Management.
    13. Ambroise Descamps & Sébastien Massoni & Lionel Page, 2022. "Learning to hesitate," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 359-383, February.
    14. Heydari, Pedram, 2021. "Luce arbitrates: Stochastic resolution of inner conflicts," Games and Economic Behavior, Elsevier, vol. 126(C), pages 33-74.
    15. Duffy, Sean & Gussman, Steven & Smith, John, 2021. "Visual judgments of length in the economics laboratory: Are there brains in stochastic choice?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).
    16. Vicky Henderson, 2012. "Prospect Theory, Liquidation, and the Disposition Effect," Management Science, INFORMS, vol. 58(2), pages 445-460, February.
    17. Alex S. L. Tse & Harry Zheng, 2019. "Speculative Trading, Prospect Theory and Transaction Costs," Papers 1911.10106, arXiv.org, revised Oct 2022.
    18. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    19. Arts, Sara & Ong, Qiyan & Qiu, Jianying, 2020. "Measuring subjective decision confidence," MPRA Paper 117907, University Library of Munich, Germany.
    20. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.

    More about this item

    Keywords

    Stochastic choice; Cautious stochastic choice; Randomization; Optimal stopping;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G39 - Financial Economics - - Corporate Finance and Governance - - - Other

    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:75:y:2023:i:3:d:10.1007_s00199-022-01428-2. 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.