Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.23685 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918076216246272 |
|---|---|
| author | Peralta, Oscar Vallejo, Habacuq |
| author_facet | Peralta, Oscar Vallejo, Habacuq |
| contents | We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like Markov-modulation and reserve-dependent parameters through an interdependent structure where the surplus level influences the dynamics of the background environment. The approach lets us define and analyze the Generalized Omega ruin model, a novel definition of insolvency that synthesizes concepts like Erlangian, cumulative Parisian and Omega ruin into a unified competing-risks framework. Finally, we show that the models are computationally tractable. By adapting recent matrix-analytic techniques, we provide an efficient way to compute a wide range of ruin-related quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hybrid Risk Processes: A Versatile Framework for Modern Ruin Problems Peralta, Oscar Vallejo, Habacuq Probability We introduce the hybrid risk process, constructed via a time-change transformation applied to the solution of a hybrid stochastic differential equation. The framework covers several modern ruin settings, incorporating features like Markov-modulation and reserve-dependent parameters through an interdependent structure where the surplus level influences the dynamics of the background environment. The approach lets us define and analyze the Generalized Omega ruin model, a novel definition of insolvency that synthesizes concepts like Erlangian, cumulative Parisian and Omega ruin into a unified competing-risks framework. Finally, we show that the models are computationally tractable. By adapting recent matrix-analytic techniques, we provide an efficient way to compute a wide range of ruin-related quantities. |
| title | Hybrid Risk Processes: A Versatile Framework for Modern Ruin Problems |
| topic | Probability |
| url | https://arxiv.org/abs/2506.23685 |