Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks

Xing-Fang Huang,Yang Yang,Tao Jiang,Ting Zhang

doi:10.3390/risks5010014

Xing-Fang Huang, Yang Yang + Show 2 more

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https://doi.org/10.3390/risks5010014

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Journal: Risks	Publication Date: Mar 3, 2017
Citations: 8	License type: CC BY 4.0

Affiliation: Nanjing Audit University, Zhejiang Gongshang University

Abstract

This paper considered a dependent discrete-time risk model, in which the insurance risks are represented by a sequence of independent and identically distributed real-valued random variables with a common Gamma-like tailed distribution; the ﬁnancial risks are denoted by another sequence of independent and identically distributed positive random variables with a ﬁnite upper endpoint, but a general dependence structure exists between each pair of the insurance risks and the ﬁnancial risks. Following the works of Yang and Yuen in 2016, we derive some asymptotic relations for the ﬁnite-time and inﬁnite-time ruin probabilities. As a complement, we demonstrate our obtained result through a Crude Monte Carlo (CMC) simulation with asymptotics.

Highlights

Consider a discrete-time risk model, where, for every i ≥ 1, the insurer’s net loss within period i is represented by a real-valued random variable (r.v.) Xi ; and the stochastic discount factor from time i to time i − 1 is denoted by a positive r.v
The first result investigates the asymptotics for the finite-time ruin probability in two cases of 0 < y∗ < 1 and y∗ = 1
We study the asymptotics for finite-time and infinite-time ruin probabilities

Summary

Introduction

Consider a discrete-time risk model, where, for every i ≥ 1, the insurer’s net loss (the aggregate claim amount minus the total premium income) within period i is represented by a real-valued random variable (r.v.) Xi ; and the stochastic discount factor from time i to time i − 1 is denoted by a positive r.v. In [17] Yang and Yuen derived some more precise results than relation (6) in the presence of Gamma-like tailed insurance risks, under the independence structure or a certain dependence structure, where each pair of the insurance risks and the financial risks follow a bivariate Sarmanov distribution (see the definition below). They investigated the asymptotic tail behavior of Sn , Mn and.

Main Results

Proofs of Main Results

Simulation Study

Conclusions