The last passage time before ruin: Theory and applications in liquidation risk management
Bibliographic record
Abstract
In response to challenges posed by emerging risks such as climate change, practitioners are increasingly aware of the need for a more forward-looking approach to insurance solvency risk management, which requires not only the identification of risks but also timely intervention. However, determining when to implement risk mitigation is often complex, as it involves balancing insolvency prevention against the potential costs and consequences of such actions. In this paper, we provide insights into the timing of risk mitigation before it is too late by studying 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 L 1 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".