Probability of ruin in discrete insurance risk model with dependent Pareto claims

Corina D Constantinescu,Tomasz J Kozubowski,Haoyu H Qian

doi:10.1515/demo-2019-0011

Corina D Constantinescu, Tomasz J Kozubowski + Show 1 more

Open Access

https://doi.org/10.1515/demo-2019-0011

Copy DOI

Abstract

Abstract We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.

Highlights

Discrete heavy-tailed distributions are an important and active area in non-life insurance research and practice
We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails
Let Θ have an absolutely continuous distribution on R+ with the cumulative distribution function (CDF) and the probability density function (PDF) denoted by FΘ and fΘ, respectively, and suppose that, given Θ = θ, the variables {Xi} of the discrete time risk model (1) are identically distributed (IID) modi ed geometric zero-modi ed geometric (ZMG)(q, ρ) with the probability mass function (PMF) (3) and ρ = − e−θ

Summary

Introduction

Discrete heavy-tailed distributions are an important and active area in non-life insurance research and practice (see, e.g., [4, 5, 21, 29]). We obtain the probability of ruin in the compound binomial risk model where the claims are zero-in ated discrete Pareto distributed and correlated by mixture.

Objectives

Results

Conclusion