Some continuity estimates for ruin probability and other ruin-related quantities

TL;DR

This paper studies the continuity properties of ruin probability in risk models, deriving estimates and inequalities for related quantities, and applying these to continuous-time surplus processes with diffusion, supported by numerical examples.

Contribution

It introduces new continuity estimates for ruin probability and related quantities in classical risk models and diffusion-perturbed processes, with iterative approximation methods.

Findings

Derived continuity estimates for ruin probability and deficit at ruin.

Established a convolution-based expression for ruin probability in diffusion models.

Provided numerical examples illustrating the theoretical results.

Abstract

In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also applied to obtain desired continuity inequalities in the setting of continuous time surplus process perturbed by diffusion. In this framework, the ruin probability can be expressed as the convolution of a compound geometric distribution $K$ with a diffusion term. A continuity inequality for $K$ is derived and an iterative approximation for this ruin-related quantity is proposed. The results are illustrated by numerical examples.