IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v93y2020icp36-49.html
   My bibliography  Save this article

Liquidation risk in insurance under contemporary regulatory frameworks

Author

Listed:
  • Li, Xin
  • Liu, Haibo
  • Tang, Qihe
  • Zhu, Jinxia

Abstract

In traditional research in insurance and finance, a firm is subject to immediate liquidation when its asset value process drops to an absorbing low barrier. This treatment greatly simplifies research but largely ignores the complexity of the liquidation procedure in the real world. In banking and finance, many researchers have taken into account the features of Chapter 7 liquidation and Chapter 11 reorganization of the U.S. Bankruptcy Code. Also, there have been similar discussions in insurance regulation, but few works have been done to achieve a quantitative understanding of the liquidation risk in insurance under contemporary regulatory frameworks. In this paper, we quantify the rehabilitation proceeding in insurance, which is akin to Chapter 11 reorganization of the U.S. Bankruptcy Code, and we conduct a probabilistic analysis of the liquidation risk of an insurance company having the option of rehabilitation. In doing so, we construct a three-barrier model to describe the solvent and insolvent states in which the surplus process follows different time-homogeneous diffusions. We derive analytical expressions for the liquidation probability and the Laplace transform of the liquidation time with a fixed grace period and then extend the study to the case with independent exponentially distributed grace periods. If further restricted to the constant elasticity of variance (CEV) framework, the obtained formulas become completely explicit.

Suggested Citation

  • Li, Xin & Liu, Haibo & Tang, Qihe & Zhu, Jinxia, 2020. "Liquidation risk in insurance under contemporary regulatory frameworks," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 36-49.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:36-49
    DOI: 10.1016/j.insmatheco.2020.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300494
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.04.005?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

    for a different version of it.

    References listed on IDEAS

    as
    1. David Landriault & Jean-François Renaud & Xiaowen Zhou, 2014. "An Insurance Risk Model with Parisian Implementation Delays," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 583-607, September.
    2. Scott E. Harrington, 2009. "The Financial Crisis, Systemic Risk, and the Future of Insurance Regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 785-819, December.
    3. Galai, Dan & Raviv, Alon & Wiener, Zvi, 2007. "Liquidation triggers and the valuation of equity and debt," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3604-3620, December.
    4. Dean Corbae & Pablo D’Erasmo, 2021. "Reorganization or Liquidation: Bankruptcy Choice and Firm Dynamics [Does Industry-wide distress Affect Defaulted Firms? Evidence from Creditor Recoveries]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(5), pages 2239-2274.
    5. Arturo Bris & Ivo Welch & Ning Zhu, 2006. "The Costs of Bankruptcy: Chapter 7 Liquidation versus Chapter 11 Reorganization," Journal of Finance, American Finance Association, vol. 61(3), pages 1253-1303, June.
    6. Yang, Chen & Sendova, Kristina P. & Li, Zhong, 2020. "Parisian ruin with a threshold dividend strategy under the dual Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 135-150.
    7. Avanzi, Benjamin & Henriksen, Lars Frederik Brandt & Wong, Bernard, 2018. "On The Distribution Of The Excedents Of Funds With Assets And Liabilities In Presence Of Solvency And Recovery Requirements," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 647-672, May.
    8. Bin Li & Qihe Tang & Lihe Wang & Xiaowen Zhou, 2014. "Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-19.
    9. Ayadi, Mohamed A. & Ben-Ameur, Hatem & Fakhfakh, Tarek, 2016. "A dynamic program for valuing corporate securities," European Journal of Operational Research, Elsevier, vol. 249(2), pages 751-770.
    10. Chen, An & Suchanecki, Michael, 2007. "Default risk, bankruptcy procedures and the market value of life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 231-255, March.
    11. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    12. Ronnie Loeffen & Irmina Czarna & Zbigniew Palmowski, 2011. "Parisian ruin probability for spectrally negative L\'{e}vy processes," Papers 1102.4055, arXiv.org, revised Mar 2013.
    13. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    14. Antill, Samuel & Grenadier, Steven R., 2019. "Optimal capital structure and bankruptcy choice: Dynamic bargaining versus liquidation," Journal of Financial Economics, Elsevier, vol. 133(1), pages 198-224.
    15. An Chen & Xia Su, 2009. "Knightian uncertainty and insurance regulation decision," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 13-33, May.
    16. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    17. Albrecher, Hansjörg & Lautscham, Volkmar, 2013. "From Ruin To Bankruptcy For Compound Poisson Surplus Processes," ASTIN Bulletin, Cambridge University Press, vol. 43(2), pages 213-243, May.
    18. Loeffen, R. & Palmowski, Z. & Surya, B.A., 2018. "Discounted penalty function at Parisian ruin for Lévy insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 190-197.
    19. Mark Broadie & Mikhail Chernov & Suresh Sundaresan, 2007. "Optimal Debt and Equity Values in the Presence of Chapter 7 and Chapter 11," Journal of Finance, American Finance Association, vol. 62(3), pages 1341-1377, June.
    20. Ya-Wen Hwang & Shih-Chieh Chang & Yang-Che Wu, 2015. "Capital Forbearance, Ex Ante Life Insurance Guaranty Schemes, and Interest Rate Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(2), pages 94-115, April.
    21. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    22. Shang-Yin Yang & Ya-Wen Hwang & Shih-Chieh Chang, 2012. "The Bankruptcy Cost of the Life Insurance Industry Under Regulatory Forbearance," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(4), pages 513-523.
    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. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Center for Mathematical Economics Working Papers 657, Center for Mathematical Economics, Bielefeld University.
    2. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org, revised Jun 2022.
    3. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    4. Aili Zhang & Ping Chen & Shuanming Li & Wenyuan Wang, 2020. "Risk Modelling on Liquidations with L\'{e}vy Processes," Papers 2007.01426, arXiv.org.
    5. Cheung, Eric C.K. & Zhu, Wei, 2023. "Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 84-101.
    6. Nataliya Vnukova & Daria Davydenko & Svitlana Achkasova & Olexandr Yagolnitskyi, 2022. "Assessing the Activities of Insurance Companies Due to the Disease of Private Pension," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 5, pages 179-194.
    7. Wenyuan Wang & Xiang Yu & Xiaowen Zhou, 2021. "On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy," Papers 2108.01800, arXiv.org, revised Nov 2023.
    8. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2022. "Optimal dividends under Markov-modulated bankruptcy level," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 146-172.
    9. Zhang, Aili & Chen, Ping & Li, Shuanming & Wang, Wenyuan, 2022. "Risk modelling on liquidations with Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    10. Lkabous, Mohamed Amine & Yang, Mengni, 2025. "Comparison results of range-based quantities in the classical risk models," Statistics & Probability Letters, Elsevier, vol. 223(C).
    11. Li, Xin, 2023. "Generalized two-barrier proportional step options," Finance Research Letters, Elsevier, vol. 51(C).

    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. Zhang, Aili & Chen, Ping & Li, Shuanming & Wang, Wenyuan, 2022. "Risk modelling on liquidations with Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Cheung, Eric C.K. & Zhu, Wei, 2023. "Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 84-101.
    3. Aili Zhang & Ping Chen & Shuanming Li & Wenyuan Wang, 2020. "Risk Modelling on Liquidations with L\'{e}vy Processes," Papers 2007.01426, arXiv.org.
    4. Nguyen, Duy Phat & Borovkov, Konstantin, 2023. "Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 72-81.
    5. Annabi, Amira & Breton, Michèle & François, Pascal, 2021. "Could Chapter 11 redeem itself? Wealth and welfare effects of the redemption option," International Review of Law and Economics, Elsevier, vol. 67(C).
    6. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    7. Dean Corbae & Pablo D’Erasmo, 2021. "Reorganization or Liquidation: Bankruptcy Choice and Firm Dynamics [Does Industry-wide distress Affect Defaulted Firms? Evidence from Creditor Recoveries]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(5), pages 2239-2274.
    8. Ran Xu & Wenyuan Wang & Jose Garrido, 2022. "Optimal Dividend Strategy Under Parisian Ruin with Affine Penalty," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1385-1409, September.
    9. Antill, Samuel & Grenadier, Steven R., 2019. "Optimal capital structure and bankruptcy choice: Dynamic bargaining versus liquidation," Journal of Financial Economics, Elsevier, vol. 133(1), pages 198-224.
    10. Roman N. Makarov, 2016. "Modeling liquidation risk with occupation times," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-11, December.
    11. Nishihara, Michi & Shibata, Takashi & Zhang, Chuanqian, 2023. "Corporate investment, financing, and exit model with an earnings-based borrowing constraint," International Review of Financial Analysis, Elsevier, vol. 85(C).
    12. Budhi Surya & Wenyuan Wang & Xianghua Zhao & Xiaowen Zhou, 2020. "Parisian excursion with capital injection for draw-down reflected Levy insurance risk process," Papers 2005.09214, arXiv.org.
    13. Lkabous, Mohamed Amine & Wang, Zijia, 2023. "On the area in the red of Lévy risk processes and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 257-278.
    14. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 280-290.
    15. Annabi, Amira & Breton, Michèle & François, Pascal, 2012. "Resolution of financial distress under Chapter 11," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1867-1887.
    16. Chang Shih-Chieh Bill & Lee Yen-Kuan, 2020. "Currency Uncertainty, Interest Guarantee, and Risk-Based Premiums in Life Insurance Guaranty Schemes," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-30, July.
    17. Giuseppe Campolieti & Hiromichi Kato & Roman N. Makarov, 2022. "Spectral Expansions for Credit Risk Modelling with Occupation Times," Risks, MDPI, vol. 10(12), pages 1-20, November.
    18. Christensen, Peter Ove & Flor, Christian Riis & Lando, David & Miltersen, Kristian R., 2014. "Dynamic capital structure with callable debt and debt renegotiations," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 644-661.
    19. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    20. Li, Xin, 2023. "Generalized two-barrier proportional step options," Finance Research Letters, Elsevier, vol. 51(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:93:y:2020:i:c:p:36-49. 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.