On a class of renewal risk model with random income

In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete K_m distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m∈?⁺). Copyright © 2008 John Wiley & Sons, Ltd.     

Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system

In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system

     

Birkhoff‐Frink representations as functors

In an earlier article we characterized, from the viewpoint of set theory, those closure operators for which the classical result of Birkhoff and Frink, stating the equivalence between algebraic closure spaces, subalgebra lattices and algebraic lattices, holds in a many‐sorted setting. In the present article we investigate, from the standpoint of category theory, the form these equivalences take when the adequate morphisms of the several different species of structures implicated in them are also taken into account. Specifically, our main aim is to provide a functorial rendering of the Birkhoff‐Frink representation theorems for both single‐sorted algebras and many‐sorted algebras, by defining the appropriate categories and functors, covariant and contravariant, involved in the process (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pattern avoidance in binary trees

This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf equivalence in which two tree patterns are equivalent if the respective n-leaf trees that avoid them are equinumerous. We investigate the equivalence classes combinatorially. Toward establishing bijective proofs of tree pattern equivalence, we develop a general method of restructuring trees that conjecturally succeeds to produce an explicit bijection for each pair of equivalent tree patterns.     

Double Series Identity and Some Laurent Type Hypergeometric Generating Relations

The main aim of this article is to obtain certain Laurent type hypergeometric generating relations. Using a general double series identity, Laurent type generating functions(in terms of Kampéde Fériet double hypergeometric function) are derived. Some known results obtained by the method of Lie groups and Lie algebras, are also modified here as special cases.     

常微分方程形式的M/M/1排队算子的谱分析

在l~1空间研究了常微分方程形式的M/M/1排队模型确定的算子A的谱问题.通过细致的谱分析,表明算子A的谱是一个椭圆型,椭圆内部点全是算子A的本征值.0位于椭圆的右边界点是边界上唯一的本征值,从而0不能与其它谱点相分离.这一结果表明常微分方程形式的M/M/1排队系统在有限时间不可能看到系统的稳定状态.     

具有随机控制函数的受控分枝过程

本文研究了具有随机控制函数的受控分枝过程的各类概率母函数间的关系.利用对概率母函数求导的方法,获得了过程的期望和方差,推广了该过程概率母函数和矩量的一些基本结果.     

Generating scenario trees: A parallel integrated simulation-optimization approach

A crucial issue for addressing decision-making problems under uncertainty is the approximate representation of multivariate stochastic processes in the form of scenario tree. This paper proposes a scenario generation approach based on the idea of integrating simulation and optimization techniques. In particular, simulation is used to generate outcomes associated with the nodes of the scenario tree which, in turn, provide the input parameters for an optimization model aimed at determining the scenarios’ probabilities matching some prescribed targets. The approach relies on the moment-matching technique originally proposed in [K. Høyland, S.W. Wallace, Generating scenario trees for multistage decision problems, Manag. Sci. 47 (2001) 295-307] and further refined in [K. Høyland, M. Kaut, S.W. Wallace, A heuristic for moment-matching scenario generation, Comput. Optim. Appl. 24 (2003) 169-185]. By taking advantage of the iterative nature of our approach, a parallel implementation has been designed and extensively tested on financial data. Numerical results show the efficiency of the parallel algorithm and the improvement in accuracy and effectiveness.     

无界时滞中立型随机微分方程解的矩估计

本文探讨了一类无界时滞的中立型随机微分方程,给出了保证所讨论的方程的整体解存在的条件,并且得到解的某种矩估计.     

双曲正弦和双曲余弦函数的幂级数余项的不等式

该文建立了双曲正弦和双曲余弦函数的幂级数余项的若干不等式.