IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v110y2023icp31-52.html
   My bibliography  Save this article

Optimal entry decision of unemployment insurance under partial information

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668723000112
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2023.02.002?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. 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 Effect of Unemployment Insurance Sanctions on the Transition Rate from Unemployment to Employment]," 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.
    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. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    2. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    3. Erik Ekström & Martin Vannestål, 2019. "American Options And Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-14, September.
    4. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    5. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    6. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.
    7. Felix Dammann & Giorgio Ferrari, 2023. "Optimal execution with multiplicative price impact and incomplete information on the return," Finance and Stochastics, Springer, vol. 27(3), pages 713-768, July.
    8. Dammann, Felix & Ferrari, Giorgio, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Center for Mathematical Economics Working Papers 663, Center for Mathematical Economics, Bielefeld University.
    9. 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.
    10. Sarah Bensalem & Nicolás Hernández-Santibáñez & Nabil Kazi-Tani, 2023. "A continuous-time model of self-protection," Finance and Stochastics, Springer, vol. 27(2), pages 503-537, April.
    11. 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.
    12. Juozas Vaicenavicius, 2017. "Asset liquidation under drift uncertainty and regime-switching volatility," Papers 1701.08579, arXiv.org, revised Jan 2019.
    13. Eisenberg, Julia & Fabrykowski, Lukas & Schmeck, Maren Diane, 2021. "Optimal Surplus-dependent Reinsurance under Regime-Switching in a Brownian Risk Model," Center for Mathematical Economics Working Papers 648, Center for Mathematical Economics, Bielefeld University.
    14. Julia Eisenberg & Lukas Fabrykowski & Maren Diane Schmeck, 2021. "Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model," Risks, MDPI, vol. 9(4), pages 1-25, April.
    15. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2021. "Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets," Papers 2105.07524, arXiv.org.
    16. 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.
    17. Ferey, Antoine, 2022. "Redistribution and Unemployment Insurance," Rationality and Competition Discussion Paper Series 345, CRC TRR 190 Rationality and Competition.
    18. Felix Dammann & Giorgio Ferrari, 2022. "Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return," Papers 2202.10414, arXiv.org, revised Nov 2022.
    19. Fu-Wei Huang & Panpan Lin & Jyh-Horng Lin & Ching-Hui Chang, 2023. "The impact of war on insurer safety: a contingent claim model analysis," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-6, December.
    20. Tiziano Angelis, 2020. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Finance and Stochastics, Springer, vol. 24(1), pages 71-123, January.

    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

    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:eee:insuma:v:110:y:2023:i:c:p:31-52. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.