重组破产下资不抵债状态的累计占位时间

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1270-1291.

重组破产下资不抵债状态的累计占位时间

明瑞星¹, 刘玉琪¹, 林陈庆¹, 王文元²^,^*()

¹ 浙江工商大学统计与数学学院杭州 310018
² 福建师范大学数学与统计学院福州 350007

收稿日期:2025-05-19 修回日期:2025-10-30 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 王文元 E-mail:wwywang@xmu.edu.cn
基金资助:
国家自然科学基金(12571508);国家自然科学基金(12171405);国家自然科学基金(11661074);福建省自然科学基金(2024J01480);浙江省登峰学科 (浙江工商大学统计学);浙江工商大学协同创新中心

On Accumulated Length of Insolvency Periods Under Reorganization Bankruptcy

Ruixing Ming¹, Yuqi Liu¹, Chenqing Lin¹, Wenyuan Wang²^,^*()

¹ School of Statistics and Mathematics, ZheJiang GongShang University, Hangzhou 310018
² School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007

Received:2025-05-19 Revised:2025-10-30 Online:2026-06-26 Published:2026-06-16
Contact: Wenyuan Wang E-mail:wwywang@xmu.edu.cn
Supported by:
NSFC(12571508);NSFC(12171405);NSFC(11661074);Natural Science Foundation of Fujian Province(2024J01480);Zhejiang Provincial Peak Discipline Program (Statistics, Zhejiang Gongshang University);Collaborative Innovation Center of Zhejiang Gongshang University

摘要/Abstract

摘要：

破产重组描述的是一种涉及债务人重组的破产形式. 该研究采用三阈值模型来描述金融机构因财务压力导致的破产情形, 模拟现实中的重组破产. 与经典破产定义 (当盈余账户余额跌破单一阈值零时即告破产) 不同, 该研究将公司的财务状况分为有偿付能力, 资不抵债和清算三种状态. 特别地, 考虑公司在资不抵债状态下采取与有偿付能力状态下不同的经营策略, 以期在监管机构规定的时间 (宽限期) 内摆脱财务困境. 若公司未能及时恢复偿付能力, 则将停止运营并进入清算状态. 通过研究清算时间和资不抵债状态占位时的联合拉普拉斯变换, 试图揭示公司金融结构与重组破产之间的内在关联.

关键词: 金融, 重组破产, 资不抵债状态累计占位时间.

Abstract:

abstract:Reorganization bankruptcy refers to a corporate rehabilitation mechanism permitting debtors to restructure operations while maintaining business continuity. This study develops a triple-threshold regulatory framework to simulate financial distress pathways in institutions mirroring real-world reorganization bankruptcy proceedings. Departing from traditional solvency assessments using a single zero-boundary criterion (where bankruptcy occurs upon falling below a single zero-value threshold), we propose a tripartite classification of financial health: solvency adequacy, insolvent or capital deficiency, and compulsory liquidation. The model's theoretical novelty lies in capturing strategic operational adjustments during capital deficiency phases to achieve regulatory compliance within "corrective grace period", with failure triggering orderly liquidation protocols. Through advanced analytical methodology involving joint Laplace transforms of liquidation timing and accumulated length of the capital deficiency durations, this research elucidates critical interdependencies between organizational capital architecture and the operational viability of reorganization-bankruptcy-style restructuring mechanisms observed in practice.

finance; reorganization bankruptcy; accumulated length of insolvency periods.

中图分类号:

O211.9

明瑞星, 刘玉琪, 林陈庆, 王文元. 重组破产下资不抵债状态的累计占位时间[J]. 数学物理学报, 2026, 46(3): 1270-1291.

Ruixing Ming, Yuqi Liu, Chenqing Lin, Wenyuan Wang. On Accumulated Length of Insolvency Periods Under Reorganization Bankruptcy[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1270-1291.

图/表 2

参考文献 24

[1]	Li X, Liu H, Tang Q, Zhu J. Liquidation risk in insurance under contemporary regulatory frameworks. Insurance: Mathematics and Economics, 2020, 93 : 36-49 doi: 10.1016/j.insmatheco.2020.04.005
[2]	Broadie M, Chernov M, Sundaresan S. Optimal debt and equity values in the presence of Chapter 7 and Chapter 11. The Journal of Finance, 2007, 62 (3): 1341-1377
[3]	Antill S, Grenadier S R. Optimal capital structure and bankruptcy choice: Dynamic bargaining versus liquidation. Journal of Financial Economics, 2019, 133 (1): 198-224 doi: 10.1016/j.jfineco.2018.05.012
[4]	Kou S G. A jump-diffusion model for option pricing. Management science, 2002, 48 (8): 1086-1101
[5]	Ramsden L, Papaioannou A D. Ruin probabilities under capital constraints. Insurance: Mathematics and Economics, 2019, 88 : 273-282 doi: 10.1016/j.insmatheco.2018.11.002
[6]	Wang W, Yu X, Zhou X. On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy. Applied Mathematics and Optimization, 2024, 89 (1): Art 13
[7]	Cai C, Li B. Occupation times of intervals until last passage times for spectrally negative Lévy processes. Journal of Theoretical Probability, 2018, 31 (4): 2194-2215 doi: 10.1007/s10959-017-0782-0
[8]	Guérin H, Renaud J F. Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view. Advances in Applied Probability, 2016, 48 (1): 274-297 doi: 10.1017/apr.2015.17
[9]	Cai N, Chen N, Wan X. Occupation times of jump-diffusion processes with double exponential jumps and the pricing of options. Mathematics of Operations Research, 2010, 35 (2): 412-437 doi: 10.1287/moor.1100.0447
[10]	Takács L. Occupation time problems in the theory of queues. Operations Research, 1964, 12 (5): 753-767 doi: 10.1287/opre.12.5.753
[11]	Bayraktar E, Young V R. Optimal investment strategy to minimize occupation time. Annals of Operations Research, 2010, 176 (1): 389-408 doi: 10.1007/s10479-008-0467-2
[12]	Densing M. Dispatch planning using newsvendor dual problems and occupation times: Application to hydropower. European Journal of Operational Research, 2013, 228 (2): 321-330 doi: 10.1016/j.ejor.2013.01.033
[13]	Frostig E, Keren-Pinhasik A. Parisian ruin with erlang delay and a lower bankruptcy barrier. Methodology and Computing in Applied Probability, 2020, 22 (1): 101-134 doi: 10.1007/s11009-019-09693-w
[14]	Jin C, Li S, Wu X. On the occupation times in a delayed Sparre Andersen risk model with exponential claims. Insurance: Mathematics and Economics, 2016, 71 : 304-316 doi: 10.1016/j.insmatheco.2016.10.001
[15]	Landriault D, Shi T. Occupation times in the MAP risk model. Insurance: Mathematics and Economics, 2015, 60 : 75-82 doi: 10.1016/j.insmatheco.2014.10.014
[16]	Kyprianou A E. Fluctuations of Lévy Processes with Applications:Introductory Lectures. Berlin: Springer Science, 2014
[17]	Ramsden L, Papaioannou A D. Ruin probabilities under capital constraints. Insurance: Mathematics and Economics, 2014, 88 : 273-282 doi: 10.1016/j.insmatheco.2018.11.002
[18]	Loeffen R L, Renaud J F, Zhou X. Occupation times of intervals until first passage times for spectrally negative Lévy processes. Stochastic Processes and their Applications, 2014, 124 (3): 1408-1435 doi: 10.1016/j.spa.2013.11.005
[19]	Landriault D, Renaud J F, Zhou X. Occupation times of spectrally negative Lévy processes with applications. Stochastic Processes and their Applications, 2011, 121 (11): 2629-2641 doi: 10.1016/j.spa.2011.07.008
[20]	Guérin H, Renaud J F. Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view. Advances in Applied Probability, 2017, 48 (1): 274-297 doi: 10.1017/apr.2015.17
[21]	Mooradian R M. The effect of bankruptcy protection on investment: chapter 11 as a screening device. The Journal of Finance, 1994, 49 (4): 1403-1430 doi: 10.1111/jofi.1994.49.issue-4
[22]	Landriault D, Li B, Lkabous M A. On occupation times in the red of Lévy risk models. Insurance: Mathematics and Economics, 2020, 92 : 17-26 doi: 10.1016/j.insmatheco.2020.02.011
[23]	Chesney M, Jeanblanc-Picqué M, Yor M. Brownian excursions and Parisian barrier options. Advances in Applied Probability, 1997, 29 : 165-184 doi: 10.2307/1427865
[24]	Kyprianou A E, Pardo J C, Pérez J L. Occupation times of refracted Lévy processes. Journal of Theoretical Probability, 2014, 27 : 1292-1315 doi: 10.1007/s10959-013-0501-4