Exponential bounds of ruin probabilities for non-homogeneous risk models

TL;DR

This paper derives exponential bounds for ruin probabilities in non-homogeneous risk models using martingale methods, introducing new models and providing broad applicability under weak assumptions.

Contribution

It presents novel exponential bounds for ruin probabilities in general non-homogeneous risk models and studies new risk models like united and quasi-periodic models with interest.

Findings

Derived exponential bounds for ruin probabilities.

Analyzed new risk models including united and quasi-periodic models.

Applied martingale methods under weak assumptions.

Abstract

Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented in this paper. By employing martingale method, the upper bounds of ruin probabilities are obtained for the general risk models under weak assumptions. In addition, several risk models, including the newly defined united risk model and quasi-periodic risk model with interest rate, are studied.