scholarly journals Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times

2017 ◽  
Vol 13 (2) ◽  
pp. 995-1007 ◽  
Author(s):  
Rongfei Liu ◽  
◽  
Dingcheng Wang ◽  
Jiangyan Peng ◽  
Keyword(s):  
Ruin Probability ◽  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Infinite Time ◽  
Arrival Times ◽  
Renewal Risk Model ◽  
Exponential Lévy Process ◽  
Renewal Risk

scholarly journals The probabilities of absolute ruin in the renewal risk model with constant force of interest

2010 ◽  
Vol 47 (2) ◽  
pp. 323-334 ◽  
Author(s):  
Dimitrios G. Konstantinides ◽  
Kai W. Ng ◽  
Qihe Tang
Keyword(s):  
Risk Model ◽  
Asymptotic Expression ◽  
Poisson Model ◽  
Weighted Sums ◽  
Constant Force ◽  
Infinite Time ◽  
Renewal Risk Model ◽  
Absolute Ruin ◽  
Force Of Interest ◽  
Renewal Risk

In this paper we consider the probabilities of finite- and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite- and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.

scholarly journals Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models

2011 ◽  
Vol 48 (A) ◽  
pp. 3-14
Author(s):  
Hansjörg Albrecher ◽  
Sem C. Borst ◽  
Onno J. Boxma ◽  
Jacques Resing
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Models ◽  
Renewal Risk Model ◽  
Insurance Portfolio ◽  
Tax Payments ◽  
Renewal Risk

In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér–Lundberg model with and without tax payments. We also provide a relation of the Cramér–Lundberg risk model with the G/G/∞ queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér– Lundberg risk model.

Precise Large Deviation of Claim Surplus Process in a Renewal Risk Model with Random Premium Income

2013 ◽  
Vol 850-851 ◽  
pp. 771-775
Author(s):  
Ying Hua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Dependence Structure ◽  
Arrival Times ◽  
Renewal Risk Model ◽  
Surplus Process ◽  
Precise Large Deviation ◽  
Renewal Risk ◽  
Premium Income

In this paper, we consider a nonstandard renewal risk model in which claim sizes and corresponding inter-arrival times form a sequence of independent and identically distributed random pairs. Each pair satisfies a certain dependence structure. In addition, premium income is described by a compound Poisson process. When the distribution of claim sizes belongs to the consistent variation class, we obtain precise large deviation of claim surplus process.

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.

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