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A uniform asymptotic estimate for discounted aggregate claims with subexponential tails
Xuemiao Hao,Qihe Tang +1 more
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In this paper, the authors studied the tail probability of discounted aggregate claims in a continuous-time renewal model and obtained an asymptotic formula, which holds uniformly for all time horizons within a finite interval.Abstract:
In this paper we study the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, we obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, we further prove that this formula holds uniformly for all time horizons. In this way, we significantly extend a recent result of Tang [Tang, Q., 2007. Heavy tails of discounted aggregate claims in the continuous-time renewal model. J. Appl. Probab. 44 (2), 285–294].read more
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Journal ArticleDOI
Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate
TL;DR: In this article, an asymptotically equivalent formula for the finite-time ruin probability of a nonstandard risk model with a constant interest rate, in which both claim sizes and inter-arrival times follow a certain dependence structure, was given.
Journal ArticleDOI
Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model
Jinzhu Li,Qihe Tang,Rong Wu +2 more
TL;DR: In this paper, the authors consider a continuous-time renewal risk model with a constant force of interest and derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure.
Journal ArticleDOI
A note on a dependent risk model with constant interest rate
Xijun Liu,Qingwu Gao,Yuebao Wang +2 more
TL;DR: For a dependent risk model with constant interest rate, in which the claim sizes form a sequence of upper tail asymptotically independent and identically distributed random variables, and their inter-arrival times are another sequence of widely lower orthant dependent as discussed by the authors.
Journal ArticleDOI
Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models
TL;DR: In this paper, uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional renewal risk models with constant interest forces and diffusion generated by Brownian motions were derived.
Journal ArticleDOI
Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims
Haizhong Yang,Jinzhu Li +1 more
TL;DR: In this paper, a bidimensional renewal risk model with constant interest force and dependent subexponential claims was considered and an explicit asymptotic formula for the finite-time ruin probability was derived.
References
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Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
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Modelling Extremal Events for Insurance and Finance
TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.
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The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
TL;DR: In this article, the authors considered continuous-time counterparts of Z and S, and derived the distribution of ∫ exp(γt-σWt )1(0, ∞) (t)dt when W is Brownian motion.
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Risk theory in a stochastic economic environment
TL;DR: In this article, the authors introduce a general model to describe the risk process of an insurance company and obtain some integro-differential equations that in some cases lead us to the exact probability of eventual ruin and in other cases to inequalities.
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