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Liquidation risk in insurance under contemporary regulatory frameworks

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  • 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
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    6. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org, revised Jun 2022.
    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. Li, Xin, 2023. "Generalized two-barrier proportional step options," Finance Research Letters, Elsevier, vol. 51(C).
    9. 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.
    10. 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.

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