Hybrid risk processes: a versatile framework for modern ruin problems

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 [Albrecher, H., & Peralta, O. (2026). Space-grid approximations of hybrid stochastic differential equations and first passage properties. To Appear in Journal of Applied Probability.], we provide an efficient way to compute a wide range of ruin-related quantities.