On joint ruin probabilities of a two-dimensional risk model with constant interest rate

TL;DR

This paper analyzes the joint ruin probabilities in a two-dimensional risk model with constant interest, deriving integral-differential equations and asymptotic formulas for finite-time ruin probabilities.

Contribution

It introduces new integral-differential equations and asymptotic expressions for joint ruin probabilities in a two-dimensional risk model with interest.

Findings

Derived integral-differential equations for Laplace transforms.

Obtained asymptotic expressions for finite-time ruin probabilities.

Extended the analysis of joint ruin times in risk models.

Abstract

In this note we consider the two-dimensional risk model introduced in Avram et al. \cite{APP08} with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite time ruin probabilities with respect to the joint ruin times $T_{\rm max}(u_1,u_2)$ and $T_{\rm min}(u_1,u_2)$ respectively.