A Lundberg-type inequality for an inhomogeneous renewal risk model

TL;DR

This paper establishes a Lundberg-type inequality for an inhomogeneous renewal risk model with non-identically distributed claim sizes and interoccurrence times, extending classical risk theory results.

Contribution

It introduces a new inequality for inhomogeneous renewal risk models, broadening the applicability of classical risk bounds to more general, non-identically distributed scenarios.

Findings

Derived a Lundberg-type inequality for inhomogeneous models

Proved an auxiliary lemma on large deviations of asymptotically drifting sums

Extended classical risk bounds to non-i.i.d. claim processes

Abstract

We obtain a Lundberg-type inequality in the case of an inhomogeneous renewal risk model. We consider the model with independent, but not necessarily identically distributed, claim sizes and the interoccurrence times. In order to prove the main theorem, we first formulate and prove an auxiliary lemma on large values of a sum of random variables asymptotically drifted in the negative direction.