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.

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.

scholarly journals Uniform Estimate of the Finite-Time Ruin Probability for All Times in a Generalized Compound Renewal Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Qingwu Gao ◽  
Na Jin ◽  
Juan Zheng
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Uniform Estimate ◽  
Random Variables ◽  
Dependence Structure ◽  
Finite Time Ruin Probability ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Compound Renewal Risk Model

We discuss the uniformly asymptotic estimate of the finite-time ruin probability for all times in a generalized compound renewal risk model, where the interarrival times of successive accidents and all the claim sizes caused by an accident are two sequences of random variables following a wide dependence structure. This wide dependence structure allows random variables to be either negatively dependent or positively dependent.

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.

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