Ruin-dependent bivariate stochastic fluid processes

TL;DR

This paper introduces a new bivariate stochastic fluid process model where a ruin event in one process triggers a behavioral change in the other, with analytical tools for ruin probabilities and joint ruin times.

Contribution

It develops a novel ruin-dependent bivariate stochastic fluid process model with a matrix-analytic approach and closed-form approximations for key ruin-related metrics.

Findings

Derived closed-form expressions for joint ruin time distributions.

Introduced a matrix-analytic framework for analyzing ruin probabilities.

Developed pathwise approximations for the process behavior.

Abstract

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, our model allows each process to operate independently until a ruin event in one triggers a change in the other. We develop a mathematical framework for our model, exploring its properties and providing closed-form expressions for approximations of key performance metrics, particularly the joint law of the ruin times. Our approach introduces a class of compatible pathwise approximations to analyze ruin probabilities, which we subsequently study through a matrix-analytic framework.