Ruin probability in the three-seasonal discrete-time risk model

TL;DR

This paper analyzes the ruin probability in a discrete-time risk model with claims repeating every three periods, providing recursive formulas and numerical examples to compute ruin probabilities.

Contribution

It introduces recursive formulas for ruin probabilities in a three-seasonal discrete-time risk model with nonidentically distributed claims.

Findings

Derived recursive formulas for ruin probabilities.

Provided numerical examples illustrating the theoretical results.

Analyzed the impact of seasonal claim patterns on ruin probability.

Abstract

This paper deals with the discrete-time risk model with nonidentically distributed claims. We suppose that the claims repeat with time periods of three units, that is, claim distributions coincide at times $\{1,4,7,\ldots\}$, at times $\{2,5,8,\ldots\}$, and at times $\{3,6,9,\ldots\}$. We present the recursive formulas to calculate the finite-time and ultimate ruin probabilities. We illustrate the theoretical results by several numerical examples.