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Consider a nonstandard compound renewal risk model with stochastic return on investments, where the price process of investment portfolio is modeled as an exponential Lévy process. In the presence of heavy tails and dependence structures among modeling components, we study the uniform asymptotics of the tail probability of stochastic discounted aggregate claims and the finite-time ruin probability for all time varying in a relevant finite or infinite interval. [ABSTRACT FROM AUTHOR]

During extreme events such as natural or man-made disasters, it is likely that after immediate claims directly caused by the events, there are other delayed claims occurring in a certain period of future. In the classical risk model, each immediate claim is accompanied with a delayed one, but in reality each immediate claim can lead to a random number of delayed ones. To this end, we consider an insurance risk model with a random number of delayed claims as well as Brownian perturbation, dependence structures and constant interest force, and explore asymptotic estimations for an insurer's ruin-related risks exposed to the extreme events. This article provides a novel insight to model and analyze the potential risks by fully considering the ongoing impacts of heavy-tailed claims, and thus accurately assesses the insurer's operation risk in the long run. [ABSTRACT FROM AUTHOR]

Abstract In this article, we consider a bidimensional risk model with strong asymptotic independence between marginal claims having consistent varying tails and study the asymptotics of precise large deviations of aggregate claims by allowing claim-size vectors and their inter-arrival times to be arbitrarily dependent. This study can provide novel insights into the various dependence structures imposed on the involved modeling components. [ABSTRACT FROM AUTHOR]

Consider a nonstandard compound renewal risk model, which is more realistic in catastrophe insurance and can extend classical risk models to the case when perhaps not only one individual claim occurs in a catastrophe such as windstorm, earthquake, epidemic, strike or riot. In the presence of heavy tails and dependence structures among modelling components, we obtain the uniform asymptotics of the tail probability of discounted aggregate claims and the finite-time ruin probability for all time varying in a relevant finite or infinite interval. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we obtain some new exponential inequalities for partial sums and their finite maximum of acceptable random variables by the results of Sung et al. (J. Korean Stat. Soc., 40, 109-114, 2011) and in different ways from theirs. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. In addition, we introduce some concepts and examples of widely acceptable random variables to extend our results mentioned above. Mathematics Subject Classification (2000) 60F15, 62G20

Recently, Jiang et al. (Statist. Probab. Lett. 101, 83–91) obtained the asymptotic formulas for the large deviations for the stochastic present value of aggregate claims in the renewal risk model with Pareto-type claims and stochastic return on investments, where the price process of the investment portfolio is described as a geometric Lévy process. In the paper, we extend the above results to a nonstandard compound renewal risk model with widely upper orthant dependent and dominatedly-varying-tailed claims. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dependent risk model, in which the claim sizes are ofdependence structure, their inter-arrival times are independent, identically distributed (i.i.d.), and the claim size and its corresponding inter-arrival time satisfy a certain dependence structure described via the conditional distribution of the inter-arrival time given the subsequent claim size being large. We obtain the asymptotics of the lower and upper bounds of precise large deviations for the aggregate amount of claims, which holds uniformly for allxin an infinite interval oft. [ABSTRACT FROM AUTHOR]