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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 non-standard renewal risk model in which each immediate claim is accompanied by a random number of delayed claims. The delayed claims capture the ongoing impacts of certain extreme events. Moreover, the model contains a perturbation by diffusion and assumes a constant force of interest. We study the tail probability of discounted aggregate claims and the ruin probability. Under the assumption that the immediate and delayed claims have subexponential tails, we derive some asymptotic formulas that hold uniformly for the time horizon varying in a finite interval. When we strengthen the assumption of subexponential tails to consistent tails, the obtained asymptotic formulas hold uniformly for the time horizon varying over an infinite interval. The uniformity is a key feature of our work. [ABSTRACT FROM AUTHOR]

As one of the security issues, privacy protection (PP) has become a research hotspot. The paper studies the synchronization problem of stochastic networks based on PP. First, a synchronization standard for stochastic network with delay is given based on PP. Second, a finite‐time (FnT) synchronization criterion for stochastic network without delay is given based on PP. The PP function of continuous time‐varying function is designed to mask the real state of the controlled complex network before converging to the real value in FnT and infinite time. Finally, the effectiveness of the method discussed in this article was verified through simulation examples. [ABSTRACT FROM AUTHOR]

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]

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

Coronavirus Disease 2019 (COVID-19) is a zoonotic illness which has spread rapidly and widely since December, 2019, and is identified as a global pandemic by the World Health Organization. The pandemic to date has been characterized by ongoing cluster community transmission. Quarantine intervention to prevent and control the transmission are expected to have a substantial impact on delaying the growth and mitigating the size of the epidemic. To our best knowledge, our study is among the initial efforts to analyze the interplay between transmission dynamics and quarantine intervention of the COVID-19 outbreak in a cluster community. In the paper, we propose a novel Transmission-Quarantine epidemiological model by nonlinear ordinary differential equations system. With the use of detailed epidemiologic data from the Cruise ship "Diamond Princess", we design a Transmission-Quarantine work-flow to determine the optimal case-specific parameters, and validate the proposed model by comparing the simulated curve with the real data. First, we apply a general SEIR-type epidemic model to study the transmission dynamics of COVID-19 without quarantine intervention, and present the analytic and simulation results for the epidemiological parameters such as the basic reproduction number, the maximal scale of infectious cases, the instant number of recovered cases, the popularity level and the final scope of the epidemic of COVID-19. Second, we adopt the proposed Transmission-Quarantine interplay model to predict the varying trend of COVID-19 with quarantine intervention, and compare the transmission dynamics with and without quarantine to illustrate the effectiveness of the quarantine measure, which indicates that with quarantine intervention, the number of infectious cases in 7 days decrease by about 60%, compared with the scenario of no intervention. Finally, we conduct sensitivity analysis to simulate the impacts of different parameters and different quarantine measures, and identify the optimal quarantine strategy that will be used by the decision makers to achieve the maximal protection of population with the minimal interruption of economic and social development. [ABSTRACT FROM AUTHOR]

The mobile networks have increasingly facilitated our daily life but are also breeding grounds for malicious worms, which are considered as the main threat to cyber security. The purpose of this paper is to analyze the dynamics of worm propagation and to control the worm epidemic based on mobile-phone networks. Accordingly, we establish an SEIQR-type model to explore the worm epidemic with saturated incidence rate. This paper shows that if the basic reproduction number is less than 1, the worm-free equilibrium is asymptotically stable, and the epidemic of worm will eventually disappear and remain under control; in addition, if the basic reproduction number is greater than 1, the asymptotical stability of worm-existence equilibrium is derived to imply that the epidemic will remain persistent and uncontrollable. Our results give new insights to mobile network security, namely, that is predicting the worm spreading tendency, identifying the epidemic control strategies, and estimating the worm popularity level. Numerical experiments are conducted to show the rationality of our obtained results and the effectiveness of the control strategies. [ABSTRACT FROM AUTHOR]

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]

In this paper we consider the tail behavior of a two-dimensional dependent renewal risk model with two dependent classes of insurance business, in which the claim sizes are governed by a common renewal counting process, and their inter-arrival times are dependent, identically distributed. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all time in an infinite interval. Moreover, we point out that the formula still holds uniformly for all time in an infinite interval for widely dependent random variables (r.v.s) under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the tail behavior of discounted aggregate claims in a dependent risk model with constant interest force, in which the claim sizes are of upper tail asymptotic independence structure, and the claim size and its corresponding inter-claim time satisfy a certain dependence structure described by a conditional tail probability of the claim size given the inter-claim time before the claim occurs. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all times in a finite interval. Moreover, we prove that if the claim size distribution belongs to the consistent variation class, the formula holds uniformly for all times in an infinite interval. [ABSTRACT FROM AUTHOR]

This article investigates the asymptotic tail probabilities of randomly weighted sums and their maximum of pairwise quasi upper-tail independent increments with non negative and arbitrarily dependent random weights. An application of the obtained results to risk theory is proposed. [ABSTRACT FROM PUBLISHER]

Mobile devices are considerably pervasive in society, but also increase their vulnerability to worm attacks from mobile networks. In this paper, we propose a new Vulnerable-Exposed-Infectious-Quarantined-Secured worm propagation model with saturated incidence and strategies of both vaccination and quarantine. We obtain that the basic reproduction number R 0 is a sharp threshold parameter such that the worm-free equilibrium is asymptotically stable for R 0 ≤ 1, implying that the worm dies out eventually and its attack remains under control; the worm-existence equilibrium is asymptotically stable when R 0 > 1, namely, the worm is always persistent and spreading within a population. This paper provides some novel insights to cyber security by that (a) the stability of worm-free equilibrium establishes the control strategies to reduce the intensity of worm attacks, and the optimal control strategy is proposed by using Pontryagins Minimum Principle; (b) the stability of worm-existence equilibrium predicts the tendency of worm propagation in a long run and assesses the level of the worm popularity by the final scale of infected devices. Numerical simulations are implemented to illustrate the feasibility of the theoretical results and the effectiveness of the control strategies. [ABSTRACT FROM AUTHOR]