Academic Report of School of Mathematical Sciences [2025] No. 119

(Series Report for High-Level University Construction No. 1221)

Title: The Last Passage Time Before Ruin: Theory and Applications in Liquidation Risk Management

Speaker: Assistant Professor Wang Zijia (The Chinese University of Hong Kong)

Time: 10:30-11:30, November 18, 2025 (Tuesday)

Location: Huiwen Building, Room 2433

Abstract:

In this paper, we study the last time a Lévy insurance risk process is above a certain threshold before ruin. In the theoretical part, we first derive the joint Laplace transform of the last passage time and the remaining time until ruin. We then study an optimal prediction problem of approximating the last passage time before ruin with a stopping time under the L¹ distance, showing that the optimum occurs when the risk process first drops below a certain level. The stopping boundary is independent of the initial surplus level, and we provide an explicit characterization of this boundary. These theoretical results fill a gap in the literature, where last passage times are typically analyzed over an infinite time horizon or an independent exponential time horizon. By focusing on the dynamics of risk processes up to ruin, our findings offer interesting insights into liquidation risk management. These are discussed in the application part, where we develop a framework to endogenously determine financial distress and rehabilitation levels under contemporary regulations. We further analyze the liquidation time under Chapter 7 and Chapter 11 of the U.S. Bankruptcy Code. Numerical examples and an empirical study using real data are presented to illustrate the practical implications of our results.

Speaker Biography:

Zijia Wang joined the Chinese University of Hong Kong (CUHK) Business School in 2022 as an Assistant Professor. Her research interests primarily focus on the quantitative analysis of insurance risk processes with applications to risk management. She is also a Fellow of the Society of Actuaries (FSA).

All faculty and students are welcome!

Host: Li Jingchao

School of Mathematical Sciences

November 14, 2025