Minimum survival probabilities in a two-dimensional risk model perturbed by diffusion

TL;DR

This paper analyzes the minimum survival probabilities over finite and infinite time horizons in a two-dimensional risk model affected by diffusion, deriving equations and explicit formulas in special cases.

Contribution

It introduces equations for survival probabilities in a 2D risk model with diffusion and provides explicit solutions in specific scenarios.

Findings

Derived equations for finite and ultimate minimum survival probabilities.

Obtained explicit expressions for ultimate survival probability in special cases.

Enhanced understanding of risk model behavior under diffusion perturbations.

Abstract

In this paper we consider the finite time minimum survival probability and ultimate minimum survival probability in a two ? dimensional risk modal perturbed by diffusion Using some properties of the minimum survival probability we obtain the equation of the finite time minimum survival probability and ultimate minimum survival probability that they are satisfied and, the explicit expressions for ultimate minimum survival probability are given in a special case.