Approximation of the fixed-probability level for a compound renewal process

TL;DR

This paper develops an analytical method based on Kendall's identity to approximate the fixed-probability level in compound renewal processes, which is crucial for risk assessment and inverse level crossing problems.

Contribution

It introduces a novel analytical technique for approximating the fixed-probability level in compound renewal processes using Kendall's identity, advancing risk theory applications.

Findings

Provides an inverse Gaussian approximation for the level crossing problem

Develops an analytical approach for fixed-probability level estimation

Enhances risk assessment methods in renewal process models

Abstract

Dealing with compound renewal process with generally distributed jump sizes and inter-renewal intervals, we focus on the approximation for the fixed-probability level, which is the core of inverse level crossing problem. We are developing an analytical technique presented in [15]-[17] and based on Kendall's identity; this yields (see [18]) inverse Gaussian approximation in the direct level crossing problem. These issues are of great importance in risk theory.