Practical approaches to the estimation of the ruin probability in a risk model with additional funds

TL;DR

This paper introduces practical methods for estimating the ruin probability in an insurance risk model with additional funds, including bounds and approximations, validated through Monte Carlo simulations.

Contribution

It presents new exponential bounds and an analogue to the De Vylder approximation for ruin probability in a generalized risk model with additional funds.

Findings

The exponential bound provides an upper estimate for ruin probability.

The De Vylder analogue offers a practical approximation method.

Monte Carlo simulations validate the effectiveness of the proposed approaches.

Abstract

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an upper exponential bound and construct an analogue to the De Vylder approximation for the ruin probability. We compare results of these approaches with statistical estimates obtained by the Monte Carlo method for selected distributions of claim sizes and additional funds.