Discrete time risk models with m-dependent random variables

TL;DR

This paper investigates ruin probabilities in discrete time risk models with m-dependent premiums and claims, extending classical results for independent sequences by incorporating dependencies and interest rates.

Contribution

It introduces new ruin probability formulas for models with m-dependent sequences, generalizing existing results to dependent cases with interest rates.

Findings

Extended ruin probability formulas for m-dependent sequences

Demonstrated impact of dependence on ruin probabilities

Generalized classical independent sequence results

Abstract

The main purpose of the paper is to study ruin probabilities in two discrete time risk models under rates of interest, where the premiums and claims are two independent sequences of m-dependent random variables, and the rate of interest is a sequence of identically distributed random variables. Our results extend the corresponding ones for independent random sequences.