ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY*

doi:10.1007/s10473-024-0112-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 215-233.doi: 10.1007/s10473-024-0112-4

ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*

Wenyuan WANG^1,2, Ruixing MING^3,†, Yijun HU⁴

1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
3. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;
4. School of Mathematics and Statistics, Wuhan University, Wuhan 430071, China

收稿日期:2022-09-18 修回日期:2023-07-23 出版日期:2024-02-25 发布日期:2024-02-27
通讯作者: † Ruixing MING, E-mail: rxming@zjgsu.edu.cn
作者简介:Wenyuan WANG, E-mail: wywang@fjnu.edu.cn; Yijun HU, E-mail: yjhu.math@whu.edu.cn
基金资助:
Wenyuan Wang acknowledges the financial support from the National Natural Science Foundation of China (12171405 and 11661074) and the Program for New Century Excellent Talents in Fujian Province University. Ruixing Ming acknowledges the financial support from the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University - Statistics), Collaborative Innovation Center of Statistical Data Engineering Technology & Application, Digital + Discipline Construction Project (SZJ2022B004).

ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*

Wenyuan WANG^1,2, Ruixing MING^3,†, Yijun HU⁴

1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
3. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China;
4. School of Mathematics and Statistics, Wuhan University, Wuhan 430071, China

Received:2022-09-18 Revised:2023-07-23 Online:2024-02-25 Published:2024-02-27
Contact: † Ruixing MING, E-mail: rxming@zjgsu.edu.cn
About author:Wenyuan WANG, E-mail: wywang@fjnu.edu.cn; Yijun HU, E-mail: yjhu.math@whu.edu.cn
Supported by:
Wenyuan Wang acknowledges the financial support from the National Natural Science Foundation of China (12171405 and 11661074) and the Program for New Century Excellent Talents in Fujian Province University. Ruixing Ming acknowledges the financial support from the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University - Statistics), Collaborative Innovation Center of Statistical Data Engineering Technology & Application, Digital + Discipline Construction Project (SZJ2022B004).

摘要/Abstract

摘要： Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S. bankruptcy code, in this paper we follow [44] to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S. Chapter 11 bankruptcy. We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments. Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem, and hence computations and proofs that are distinct from [44] are needed. To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy, the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching. Some explicit expressions of the expected net present values under a double barrier dividend strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies. When the tail of the Lévy measure is log-convex, this optimal double barrier dividend strategy is then verified as the optimal dividend strategy, solving our optimal impulse control problem.

关键词: spectrally negative Lévy process, Chapter 11 bankruptcy, De Finetti's dividend problem, double barrier strategy, impulse control

Abstract: Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S. bankruptcy code, in this paper we follow [44] to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S. Chapter 11 bankruptcy. We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments. Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem, and hence computations and proofs that are distinct from [44] are needed. To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy, the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching. Some explicit expressions of the expected net present values under a double barrier dividend strategy, new to the literature, are established in terms of scale functions. With the help of these expressions, we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies. When the tail of the Lévy measure is log-convex, this optimal double barrier dividend strategy is then verified as the optimal dividend strategy, solving our optimal impulse control problem.

Key words: spectrally negative Lévy process, Chapter 11 bankruptcy, De Finetti's dividend problem, double barrier strategy, impulse control

中图分类号:

60G51

Wenyuan WANG, Ruixing MING, Yijun HU. ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*[J]. 数学物理学报(英文版), 2024, 44(1): 215-233.

Wenyuan WANG, Ruixing MING, Yijun HU. ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*[J]. Acta mathematica scientia,Series B, 2024, 44(1): 215-233.

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ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*

ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY^*

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