scholarly journals Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

2010 ◽  
Vol 46 (2) ◽  
pp. 362-370 ◽  
Author(s):  
Qihe Tang ◽  
Guojing Wang ◽  
Kam C. Yuen
Keyword(s):  
Risk Model ◽  
Tail Asymptotics ◽  
Present Value ◽  
Renewal Risk Model ◽  
Aggregate Claims ◽  
Renewal Risk

Beta transform and discounted aggregate claims under dependency

2018 ◽  
Vol 13 (2) ◽  
pp. 241-267
Author(s):  
Zhehao Zhang ◽  
Shuanming Li
Keyword(s):  
Risk Model ◽  
Stochastic Ordering ◽  
Joint Moments ◽  
Numerical Examples ◽  
Renewal Risk Model ◽  
Recursive Formulas ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
Compound Renewal Risk Model

AbstractThis paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical examples are provided to illustrate our results.

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.

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