Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims

This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution, we derive for the finite-time ruin probability an explicit asymptotic formula.     

On the ruin probabilities of a bidimensional perturbed risk model

We follow some recent works to study the ruin probabilities of a bidimensional perturbed insurance risk model. For the case of light-tailed claims, using the martingale technique we obtain for the infinite-time ruin probability a Lundberg-type upper bound, which captures certain information of dependence between the two marginal surplus processes. For the case of heavy-tailed claims, we derive for the finite-time ruin probability an explicit asymptotic estimate.     

Tail asymptotics for the queue length in an M/G/1 retrial queue

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue. AMS subject classifications: 60J25, 60K25     

The subexponentiality of products revisited

Following the work of Cline and Samorodnitsky (Stoch. Process. Their Appl. 49(1):75–98, 1994), we reexamine the subexponentiality of the product of two random variables, X and Y, which are independent and have distributions F and G, respectively. The main result is the following: If F belongs to the class [that is to say, F is subexponential and holds for some v>1] and G, with G(0–)=0 and G(0)<0, satisfies for each u>0, then the distribution of XY also belongs to the class .      

Max-sum equivalence of conditionally dependent random variables

In this paper, we prove the max-sum equivalence of random variables satisfying two conditional dependence assumptions. Besides, we also discuss the interrelationship between the above two conditional dependence assumptions. The obtained results improve and generalize some existing results.     

Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for instances with genus and underlying finite field satisfying for a positive constant is given by

The algorithm works over any finite field, and its running time does not rely on any unproven assumptions.

     

关于GI/G/1/∞排队系统的平稳等待时间分布的局部尾等价式

关于GI/G/1/∞排队系统的平稳等待时间分布W,已有许多经典的结果描述了其尾分布[AKW-](x)=1-W(x)的等价极限情况.该文结合一些保险与金融领域重要的风险变量,研究了关于分布W的各种局部尾等价式问题.