Hybrid Risk Processes: A Versatile Framework for Modern Ruin Problems
Abstract
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.
Keywords
Cite
@article{arxiv.2506.23685,
title = {Hybrid Risk Processes: A Versatile Framework for Modern Ruin Problems},
author = {Oscar Peralta and Habacuq Vallejo},
journal= {arXiv preprint arXiv:2506.23685},
year = {2025}
}