IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i3p94-d262848.html
   My bibliography  Save this article

Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance

Author

Listed:
  • Jason S. Anquandah

    (Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Leonid V. Bogachev

    (Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

Abstract

Managing unemployment is one of the key issues in social policies. Unemployment insurance schemes are designed to cushion the financial and morale blow of loss of job but also to encourage the unemployed to seek new jobs more proactively due to the continuous reduction of benefit payments. In the present paper, a simple model of unemployment insurance is proposed with a focus on optimality of the individual’s entry to the scheme. The corresponding optimal stopping problem is solved, and its similarity and differences with the perpetual American call option are discussed. Beyond a purely financial point of view, we argue that in the actuarial context the optimal decisions should take into account other possible preferences through a suitable utility function. Some examples in this direction are worked out.

Suggested Citation

  • Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance," Risks, MDPI, vol. 7(3), pages 1-41, September.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:3:p:94-:d:262848
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/3/94/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/7/3/94/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Fredriksson & Bertil Holmlund, 2006. "Optimal unemployment insurance design: Time limits, monitoring, or workfare?," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 13(5), pages 565-585, September.
    2. 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.
    3. Acemoglu, Daron & Shimer, Robert, 2000. "Productivity gains from unemployment insurance," European Economic Review, Elsevier, vol. 44(7), pages 1195-1224, June.
    4. Gabriele Stabile, 2006. "Optimal Timing Of The Annuity Purchase: Combined Stochastic Control And Optimal Stopping Problem," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 151-170.
    5. Camille Landais & Arash Nekoei & Peter Nilsson & David Seim & Johannes Spinnewijn, 2021. "Risk-Based Selection in Unemployment Insurance: Evidence and Implications," American Economic Review, American Economic Association, vol. 111(4), pages 1315-1355, April.
    6. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    7. Jang, Bong-Gyu & Park, Seyoung & Rhee, Yuna, 2013. "Optimal retirement with unemployment risks," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3585-3604.
    8. Dhami, Sanjit, 2016. "The Foundations of Behavioral Economic Analysis," OUP Catalogue, Oxford University Press, number 9780198715535.
    9. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    10. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467, April.
    11. Jonas Kolsrud & Camille Landais & Peter Nilsson & Johannes Spinnewijn, 2018. "The Optimal Timing of Unemployment Benefits: Theory and Evidence from Sweden," American Economic Review, American Economic Association, vol. 108(4-5), pages 985-1033, April.
    12. Borch, Karl, 1961. "The Utility Concept Applied to the Theory of Insurance," ASTIN Bulletin, Cambridge University Press, vol. 1(5), pages 245-255, July.
    13. Tan Wang & Tony S. Wirjanto, 2016. "Risk Aversion, Uncertainty, Unemployment Insurance Benefit and Duration of "Wait" Unemployment," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 1-34, May.
    14. Bertil Holmlund, 1998. "Unemployment Insurance in Theory and Practice," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 113-141, March.
    15. Hopenhayn, Hugo A & Nicolini, Juan Pablo, 1997. "Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 412-438, April.
    16. repec:bla:scandj:v:100:y:1998:i:1:p:113-41 is not listed on IDEAS
    17. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, October.
    18. Russell Gerrard & Bjarne Højgaard & Elena Vigna, 2012. "Choosing the optimal annuitization time post-retirement," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1143-1159, September.
    19. Vicky Henderson & David Hobson, 2008. "An explicit solution for an optimal stopping/optimal control problem which models an asset sale," Papers 0806.4061, arXiv.org, revised Nov 2008.
    20. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
    21. Erik Ekström & Bing Lu, 2011. "Optimal Selling of an Asset under Incomplete Information," International Journal of Stochastic Analysis, Hindawi, vol. 2011, pages 1-17, December.
    22. Yolanda Rebollo-Sanz & J. García-Pérez, 2015. "Are unemployment benefits harmful to the stability of working careers? The case of Spain," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(1), pages 1-41, March.
    23. Theptida Sopraseuth & Sebastien Menard & Francois Langot & Jean-Olivier Hairault, 2007. "Optimal unemployment insurance in a life cycle model," 2007 Meeting Papers 422, Society for Economic Dynamics.
    24. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521890779, October.
    25. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    26. Alain Gubian & Stéphane Jugnot & Frédéric Lerais & Vladimir Passeron, 2004. "Les effets de la RTT sur l'emploi : des estimations ex ante aux évaluations ex post," Économie et Statistique, Programme National Persée, vol. 376(1), pages 25-54.
    27. Stéphane Villeneuve, 2007. "On the Threshold Strategies and Smooth-Fit Principle For Optimal Stopping Problems," Post-Print hal-00173165, HAL.
    28. Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521813853, October.
    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. Rich Ryan, 2023. "Discretionary Extensions to Unemployment Insurance Compensation and Some Potential Costs for a McCall Worker," Risks, MDPI, vol. 11(10), pages 1-39, September.
    2. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.

    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. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Model of Unemployment Insurance," Papers 1902.06175, arXiv.org, revised Sep 2019.
    2. Mesén Vargas, Juliana & Van der Linden, Bruno, 2017. "Is There Always a Trade-off between Insurance and Incentives? The Case of Unemployment with Subsistence Constraints," IZA Discussion Papers 11034, Institute of Labor Economics (IZA).
    3. Andriy Zapechelnyuk & Ro’i Zultan, 2020. "Job search costs and incentives," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 181-202, October.
    4. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    5. Peter Fredriksson & Bertil Holmlund, 2006. "Improving Incentives in Unemployment Insurance: A Review of Recent Research," Journal of Economic Surveys, Wiley Blackwell, vol. 20(3), pages 357-386, July.
    6. Vargas Juliana Mesén & Linden Bruno Van der, 2019. "Why Cash Transfer Programs Can Both Stimulate and Slow Down Job Finding," IZA Journal of Labor Economics, Sciendo & Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 8(1), pages 1-27, June.
    7. Chae, Jiwon & Jang, Bong-Gyu & Park, Seyoung, 2023. "Analytic approach for models of optimal retirement with disability risk," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 68-75.
    8. Raj Chetty, 2008. "Moral Hazard vs. Liquidity and Optimal Unemployment Insurance," NBER Working Papers 13967, National Bureau of Economic Research, Inc.
    9. Kyyrä, Tomi & Pesola, Hanna & Rissanen, Aarne, 2017. "Unemployment Insurance in Finland: A Review of Recent Changes and Empirical Evidence on Behavioral Responses," Research Reports 184, VATT Institute for Economic Research.
    10. Nicholas Lawson, 2023. "Optimal unemployment policy," Economic Inquiry, Western Economic Association International, vol. 61(3), pages 675-692, July.
    11. Park, Seyoung, 2015. "A generalization of Yaari’s result on annuitization with optimal retirement," Economics Letters, Elsevier, vol. 137(C), pages 17-20.
    12. Johannes Spinnewijn, 2020. "The Trade‐Off between Insurance and Incentives in Differentiated Unemployment Policies," Fiscal Studies, John Wiley & Sons, vol. 41(1), pages 101-127, March.
    13. Robert Shimer & Iván Werning, 2007. "Reservation Wages and Unemployment Insurance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1145-1185.
    14. Saez, Emmanuel & Landais, Camille & Michaillat, Pascal, 2010. "Optimal Unemployment Insurance over the Business Cycle," CEPR Discussion Papers 8132, C.E.P.R. Discussion Papers.
    15. Hassler, John & Rodríguez Mora, José V., 2008. "Unemployment insurance design: Inducing moving and retraining," European Economic Review, Elsevier, vol. 52(5), pages 757-791, July.
    16. Fuller, David L. & Kudlyak, Marianna & Lkhagvasuren, Damba, 2014. "Productivity insurance: The role of unemployment benefits in a multi-sector model," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 39-53.
    17. Reichling, Felix, 2006. "Optimal Unemployment Insurance in Labor Market Equilibrium when Workers can Self-Insure," MPRA Paper 5362, University Library of Munich, Germany, revised 16 Oct 2007.
    18. Fredriksson, Peter & Holmlund, Bertil, 2001. "Optimal Unemployment Insurance in Search Equilibrium," Journal of Labor Economics, University of Chicago Press, vol. 19(2), pages 370-399, April.
    19. Konstantinos Tatsiramos & Jan C. Ours, 2014. "Labor Market Effects Of Unemployment Insurance Design," Journal of Economic Surveys, Wiley Blackwell, vol. 28(2), pages 284-311, April.
    20. Johannes F. Schmieder & Till von Wachter, 2016. "The Effects of Unemployment Insurance Benefits: New Evidence and Interpretation," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 547-581, October.

    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:gam:jrisks:v:7:y:2019:i:3:p:94-:d:262848. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.