On dividend strategies with non-exponential discounting

In this paper, we study the dividend maximization problem with a non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to Markov strategies. This is a time inconsistent control problem. The equilibrium HJB-equation is given and the verification theorem is proven for a general discount function. Considering a mixture of exponential discount functions and a pseudo-exponential discount function, we get equilibrium dividend strategies and the corresponding equilibrium value functions by solving the equilibrium HJB-equations.     

An extended multi-anticipative delay model of traffic flow

An extended multi-anticipative delay model is proposed by introducing multiple velocity differences and incorporating the reaction-time delay of drivers. The stability condition of the new model is obtained by applying the linear stability theory, and the modified Korteweg–de Vries (mKdV) equation is derived by the use of the nonlinear analysis method. The analytical and numerical results show that both the reaction-time delay of drivers and the information of multiple velocity differences have an important influence on the stability of the model, and that the stabilization of traffic flow is enhanced by appending the velocity difference information of multiple vehicles ahead or by decreasing the delay time.     

有超车规则的交通流的元胞自动机模型

分析和评论了2014年美国大学生数学建模竞赛（MCM）A题,以及获得outstanding winner奖的6篇论文。首先对试题进行分析,并结合已有文献指出A题的主要解题思路;然后,通过评述获奖论文,指出学生论文的优点及存在的问题;最后,对今年赛题的某些问题进行讨论。     

Asymptotics of Christoffel functions on arcs and curves

For a system of smooth Jordan curves and arcs asymptotics for Christoffel functions is established. A separate new method is developed to handle the upper and lower estimates. In the course to the upper bound a theorem of Widom on the norm of Chebyshev polynomials is generalized.     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

An Ant Colony Optimisation algorithm for solving the asymmetric traffic assignment problem

In this paper we propose an Ant Colony Optimisation (ACO) algorithm for defining the signal settings on urban networks following a local approach. This consists in optimising the signal settings of each intersection of an urban network as a function only of traffic flows at the accesses to the same intersection, taking account of the effects of signal settings on costs and on user route choices. This problem, also known as Local Optimisation of Signal Settings (LOSS), has been widely studied in the literature and can be formulated as an asymmetric assignment problem. The proposed ACO algorithm is based on two kinds of behaviour of artificial ants which allow the LOSS problem to be solved: traditional behaviour based on the response to pheromones for simulating user route choice, and innovative behaviour based on the pressure of an ant stream for solving the signal setting definition problem. Our results on real-scale networks show that the proposed approach allows the solution to be obtained in less time but with the same accuracy as in traditional MSA (Method of Successive Averages) approaches.     

Convergence to equilibrium states for fluid models of many-server queues with abandonment

Fluid models, in particular their equilibrium states, have become an important tool for the study of many-server queues with general service and patience time distributions. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under some conditions. Our method builds on the framework of measure-valued processes, which keeps track of the remaining patience and service times.     

利用小车的上班族在拥有辐射环状交通网络的城市工作区内通勤时的平均移动距离

在一拥有辐射环状交通网络的城市工作区内,使用小车上下班的职员在通勤时的平均移动距离约为多少？本文基于一个较现实的模型对此进行了理论上的解析,所得结果,从城市规划的观点来看,具有一定的实际意义。