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Optimal Stopping and Utility in a Simple Model of Unemployment Insurance

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  • Jason S. Anquandah
  • Leonid V. Bogachev

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 pro-actively 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 Model of Unemployment Insurance," Papers 1902.06175, arXiv.org, revised Sep 2019.
  • Handle: RePEc:arx:papers:1902.06175
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    File URL: http://arxiv.org/pdf/1902.06175
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    References listed on IDEAS

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    1. Camille Landais & Arash Nekoei & Peter Nilsson & David Seim & Johannes Spinnewijn, 2017. "Risk-based Selection in Unemployment Insurance: Evidence and Implications," STICERD - Public Economics Programme Discussion Papers 33, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Acemoglu, Daron & Shimer, Robert, 2000. "Productivity gains from unemployment insurance," European Economic Review, Elsevier, vol. 44(7), pages 1195-1224, June.
    3. 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.
    4. Holmlund, Bertil, 1998. " Unemployment Insurance in Theory and Practice," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 113-141, March.
    5. Baily, Martin Neil, 1978. "Some aspects of optimal unemployment insurance," Journal of Public Economics, Elsevier, vol. 10(3), pages 379-402, December.
    6. Borch, Karl, 1961. "The Utility Concept Applied to the Theory of Insurance," ASTIN Bulletin, Cambridge University Press, vol. 1(5), pages 245-255, July.
    7. 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.
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    9. Dhami, Sanjit, 2016. "The Foundations of Behavioral Economic Analysis," OUP Catalogue, Oxford University Press, number 9780198715535.
    10. 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.
    11. 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.
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    14. 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.
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    18. Kyoung Jin Choi & Gyoocheol Shim, 2006. "Disutility, Optimal Retirement, And Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 443-467, April.
    19. 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.
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