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Optimal entry decision of unemployment insurance under partial information

Author

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  • Xing, Jie
  • Ma, Jingtang
  • Yang, Wensheng

Abstract

The aim of this paper is to study the optimal time for the individual to join an unemployment insurance scheme which is intended to protect workers against the consequences of job loss and to encourage the unemployed workers to find a new job as early as possible. The wage dynamic is described by a geometric Brownian motion model under drift uncertainty and the problem is a kind of two-dimensional degenerate optimal stopping problems which is hard to analyze. The optimal time of decision for the workers is given by the first time at which the wage process hits the free boundary which therefore plays a key role in solving the problem. This paper analyzes the monotonicity and continuity of the free boundary and derives a nonlinear integral equation for it. For a particular case the closed-form formula of free boundary is obtained and for the general case the free boundary is solved by the numerical solution of the nonlinear integral equation. The key in the analysis is to convert the degenerate problem into the non-degenerate one using the probability approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:110:y:2023:i:c:p:31-52
    DOI: 10.1016/j.insmatheco.2023.02.002
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    References listed on IDEAS

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    1. 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.
    2. Matteo Brachetta & Claudia Ceci, 2019. "A BSDE-based approach for the optimal reinsurance problem under partial information," Papers 1910.05999, arXiv.org, revised May 2020.
    3. 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.
    4. Regis Barnichon & Yanos Zylberberg, 2022. "A Menu of Insurance Contracts for the Unemployed," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 118-141.
    5. Bertil Holmlund, 1998. "Unemployment Insurance in Theory and Practice," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 113-141, March.
    6. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    7. Jie Xiong & Zuo Quan Xu & Jiayu Zheng, 2021. "Mean–variance portfolio selection under partial information with drift uncertainty," Quantitative Finance, Taylor & Francis Journals, vol. 21(9), pages 1461-1473, September.
    8. Francesca Biagini & Jan Widenmann, 2012. "Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-32.
    9. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    10. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    11. 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.
    12. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 14, pages 327-347, World Scientific Publishing Co. Pte. Ltd..
    13. Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    14. Wei, Jiaqin & Wang, Rongming & Yang, Hailiang, 2012. "Optimal surrender strategies for equity-indexed annuity investors with partial information," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1251-1258.
    15. 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.
    16. Hugo A. Hopenhayn & Juan Pablo Nicolini, 2009. "Optimal Unemployment Insurance and Employment History," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1049-1070.
    17. Brachetta, M. & Ceci, C., 2020. "A BSDE-based approach for the optimal reinsurance problem under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 1-16.
    18. Zuo Quan Xu & Fahuai Yi, 2020. "Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 384-401, February.
    19. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2017. "Unit-linked life insurance policies: Optimal hedging in partially observable market models," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 149-163.
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    More about this item

    Keywords

    Unemployment insurance; Drift uncertainty; Free boundary; Optimal stopping; Integral equation;
    All these keywords.

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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