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

Risks ◽  
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.

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

2010 ◽  
Vol 42 (4) ◽  
pp. 1126-1146 ◽  
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.

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

2010 ◽  
Vol 42 (04) ◽  
pp. 1126-1146 ◽  
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.

scholarly journals Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

2014 ◽  
Vol 51 (3) ◽  
pp. 669-684 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Lévy Process ◽  
Tail Probability ◽  
Levy Process ◽  
Insurance Company ◽  
Risk Models ◽  
Heavy Tailed Distributions ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Heavy Tailed ◽  
Renewal Risk

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

scholarly journals Precise large deviations for the aggregate claims in a dependent compound renewal risk model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kaiyong Wang ◽  
Lamei Chen
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Precise Large Deviations ◽  
Renewal Risk Model ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
Distribution Class ◽  
Compound Renewal Risk Model

Abstract We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.

Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

2014 ◽  
Vol 51 (03) ◽  
pp. 669-684 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Lévy Process ◽  
Tail Probability ◽  
Levy Process ◽  
Insurance Company ◽  
Risk Models ◽  
Heavy Tailed Distributions ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Heavy Tailed ◽  
Renewal Risk

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

Transform approach for discounted aggregate claims in a risk model with descendant claims

2019 ◽  
Vol 293 (1) ◽  
pp. 175-192
Author(s):  
Hyunjoo Yoo ◽  
Bara Kim ◽  
Jeongsim Kim ◽  
Jiwook Jang
Keyword(s):  
Risk Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims
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