This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, the presented model allows each process to operate independently until a ruin event in one triggers a change in the other. Here, each process evolves on the entire real line (unbounded), and ruin occurs when an individual process hits level zero from above for the first time. A mathematical framework for the model is developed, to explore its properties and provide closed-form expressions for approximations of key performance metrics, particularly the joint law of the ruin times. This approach introduces a class of compatible pathwise approximations to analyze ruin probabilities, which are subsequently studied through a matrix-analytic framework. A numerical section illustrates the application of the methodology, including an analysis of the approximation’s convergence and the behavior of joint ruin probabilities.

We investigate the problem of using a Riemannian sum with random subintervals to approximate the iterated Itô integral ∫wdw - or, equivalently, solving the corresponding stochastic differential equation by Euler's method with variable step sizes. In the past this task has been used as a counterexample to illustrate that variable step sizes must be used with extreme caution in stochastic numerical analysis. This article establishes a class of variable step size schemes which do work.