Uniformly asymptotic behavior for the tail probability of discounted aggregate claims in the time-dependent risk model with upper tail asymptotically independent claims

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

Download Full-text

Uniform asymptotic behavior of tail probability of maxima in a time-dependent renewal risk model

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2019.1626429 ◽

2019 ◽

Vol 49 (24) ◽

pp. 6112-6120

Author(s):

Fotios Loukissas

Keyword(s):

Asymptotic Behavior ◽

Risk Model ◽

Tail Probability ◽

Time Dependent ◽

Renewal Risk Model ◽

Renewal Risk

Download Full-text

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Advances in Applied Probability ◽

10.1017/s0001867800004559 ◽

2010 ◽

Vol 42 (04) ◽

pp. 1126-1146 ◽

Cited By ~ 11

Author(s):

Jinzhu Li ◽

Qihe Tang ◽

Rong Wu

Keyword(s):

Asymptotic Formula ◽

Risk Model ◽

Tail Probability ◽

Dependence Structure ◽

Claim Size ◽

Claim Size Distribution ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Renewal Risk ◽

The Impact

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

Download Full-text

Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model

Risks ◽

10.3390/risks9070122 ◽

2021 ◽

Vol 9 (7) ◽

pp. 122

Author(s):

Franck Adékambi ◽

Kokou Essiomle

Keyword(s):

Risk Model ◽

Tail Probability ◽

Closed Form Expression ◽

Dependence Structure ◽

Risk Models ◽

Occurrence Time ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Force Of Interest ◽

Asymptotic Tail Probability

In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim sizes. This dependence structure is relevant since it is well known that under catastrophic or extreme events the inter-occurrence time and the claim severities are dependent.

Download Full-text