Moments of the Discounted Aggregate Claims with Delay Inter-Occurrence Distribution and Dependence Introduced by a FGM Copula

Aggregate Claims ◽

Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Uniform asymptotics for discounted aggregate claims in dependent multi-risk model

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2017.1417435 ◽

2018 ◽

Vol 48 (4) ◽

pp. 781-793

Author(s):

Dawei Lu ◽

Lixin Song ◽

Fuqi Li

Keyword(s):

Risk Model ◽

Uniform Asymptotics ◽

Tail behavior for the sum of two correlated classes of discounted aggregate claims in a time-dependent risk model

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2014.1000499 ◽

2016 ◽

Vol 46 (5) ◽

pp. 2559-2570

Author(s):

Ke-Ang Fu ◽

Jie Li

Keyword(s):

Risk Model ◽

Time Dependent ◽

Tail Behavior ◽

Asymptotic Behavior of Discounted Aggregate Claims in a Nonstandard Two-dimensional Risk Model with Dependent Claim Sizes

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/790/1/012131 ◽

2020 ◽

Vol 790 ◽

pp. 012131

Author(s):

Yinghua Dong

Keyword(s):

Asymptotic Behavior ◽

Risk Model ◽

Two Dimensional ◽

Moments of discounted aggregate claims with dependence based on Spearman copula

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112889 ◽

2020 ◽

Vol 377 ◽

pp. 112889

Author(s):

Weiwei Sun ◽

Xiang Hu ◽

Lianzeng Zhang

Keyword(s):

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

Annals of Operations Research ◽

10.1007/s10479-019-03392-y ◽

2019 ◽

Vol 293 (1) ◽

pp. 175-192

Author(s):

Hyunjoo Yoo ◽

Bara Kim ◽

Jeongsim Kim ◽

Jiwook Jang

Keyword(s):

Risk Model ◽

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

Advances in Applied Probability ◽

10.1239/aap/1293113154 ◽

2010 ◽

Vol 42 (4) ◽

pp. 1126-1146 ◽

Cited By ~ 80

Author(s):

Jinzhu Li ◽

Qihe Tang ◽

Rong Wu

Keyword(s):

Asymptotic Formula ◽

Risk Model ◽

Tail Probability ◽

Dependence Structure ◽

Claim Size ◽

Claim Size Distribution ◽

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.

Beta transform and discounted aggregate claims under dependency

Annals of Actuarial Science ◽

10.1017/s1748499518000209 ◽

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 ◽

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.