The influence of Hall current in a circular duct

In this paper, we consider the unsteady flow of an incompressible second grade fluid in a circular duct with a given volume flow rate variation. The effects of Hall current are taken into account. The governing equations are solved analytically using Laplace transform method. The velocity profiles are constructed for the four cases: (a) constant accelerated flow (b) sudden started flow (c) the flow rate has a trapezoidal variation with time (d) starting from rest the volume flow rate oscillates sinusoidally. The present analysis is more general than any previous investigation.     

An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting

An economic order quantity (EOQ) inventory model for deteriorating goods is developed with a linear, positive trend in demand allowing inventory shortages and backlogging. The effects of inflation and the time-value of money are incorporated into the model, considering two separate inflation rates: namely, the internal (company) inflation rate and the external (general economy) inflation rate. It is assumed that the goods in the inventory deteriorate over time at a constant rate θ. The inventory policy is discussed over a finite time-horizon with several reorder points. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. Several particular cases of the model are discussed in brief.     

Discrete-time Metapopulation Dynamics and Unidirectional Dispersal

The effects of unidirectional dispersal on single pioneer species discrete-time metapopulations where the pre-dispersal local patch dynamics are of the same (compensatory or overcompensatory) or mixed (compensatory and overcompensatory) types are studied. Single-species unidirectional metapopulation models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and the dispersal rate is low. The pioneer species goes extinct in at least one patch when the dispersal rate is high, while it persists when the rate is low. Unidirectional dispersal can generate multiple attractors with fractal basin boundaries whenever the pre-dispersal local patch dynamics are overcompensatory, and is capable of altering the local patch dynamics in mixed systems from compensatory to overcompensatory dynamics and vice versa.     

The impact of loyalty and promotion effects on retention rate

Researching customer retention rates is made difficult because of the lack of suitable systems with which to measure it. From a first-order Markov brand-switching model, serial equations are derived to estimate the retention rate using market share and loyalty. To explore the impact of loyalty and promotion programme on retention rate, data from five leading brands for three product categories were obtained to fit the developed model. Findings suggest that: (1) when the loyalty effect remains unchanged over a period of time, the greater the effect of a promotion programme, the greater the retention rate; (2) when the promotion effects among brands are similar, the retention rate varies depending on level of loyalty; and (3) when the proportion of loyal customers is high, the proportion of potential switchers affected by promotion programmes is low. In this case, the impact of a promotion programme on the retention rate is not significant. This model successfully demonstrates how the Markov brand-switching model can be employed to estimate a measure of retention rate from consumer panel data as well as to better understand how promotion affects loyalty, switching behaviour, and retention rate.     

Asymptotically optimal importance sampling for Jackson networks with a tree topology

This note describes an importance sampling (IS) algorithm to estimate buffer overflows of stable Jackson networks with a tree topology. Three new measures of service capacity and traffic in Jackson networks are introduced and the algorithm is defined in their terms. These measures are effective service rate, effective utilization and effective service-to-arrival ratio of a node. They depend on the nonempty/empty states of the queues of the network. For a node with a nonempty queue, the effective service rate equals the node’s nominal service rate. For a node i with an empty queue, it is either a weighted sum of the effective service rates of the nodes receiving traffic directly from node i, or the nominal service rate, whichever smaller. The effective utilization is the ratio of arrival rate to the effective service rate and the effective service-to-arrival ratio is its reciprocal. The rare overflow event of interest is the following: given that initially the network is empty, the system experiences a buffer overflow before returning to the empty state. Two types of buffer structures are considered: (1) a single system-wide buffer shared by all nodes, and (2) each node has its own fixed size buffer. The constructed IS algorithm is asymptotically optimal, i.e., the variance of the associated estimator decays exponentially in the buffer size at the maximum possible rate. This is proved using methods from (Dupuis et al. in Ann. Appl. Probab. 17(4):1306–1346, 2007), which are based on a limit Hamilton–Jacobi–Bellman equation and its boundary conditions and their smooth subsolutions. Numerical examples involving networks with as many as eight nodes are provided.     

分段时变参数CIR模型及其实证研究

经济环境总体是变化的,但在一定阶段会保持局部稳定.鉴于此,提出了分段时变参数CIR模型的构想,并用它来建模短期利率与汇率.给出了CIR模型设定检验的广义残差拟合优度检验法,用之来检验模型的时变性.用数值模拟和实证分析来验证分段时变参数CIR模型进行利率、汇率建模的可行性和合理性.数值模拟表明,两组符合CIR(Cox-Ingersoll-Ross)模型的数据合在一起不一定还符合CIR模型.通过对短期国库券利率和加拿大元与美元汇率数据的实证分析,发现用分段时变参数CIR模型来描述短期利(汇)率比一般的固定常数CIR模型更加合理.     

On optimal service capacity allocation policy in an advance selling environment in continuous time

Based on some general reasonable assumptions, this paper employs the techniques of calculus of variations and optimal control theory to derive 10 main propositions associated with a service provider who aims at maximizing the present value of revenues/profits over a planning horizon in continuous time. Employing an aggregate pricing-response function that is dependent on excess capacity and a convex service cost formulation, the results show that (i) for a zero discount rate and unanticipated competitive entry, units of service capacity are allocated evenly over time, (ii) for a zero discount rate and anticipated competitive entry, units of allocated service capacity are increasing over time, (iii) for a positive discount rate and unanticipated competitive entry, units of allocated service capacity are decreasing over time, and (iv) for a positive discount rate and anticipated competitive entry, units of allocated service capacity are increasing over time, or are decreasing at first then increasing later. In addition, the questions of how deep a service firm should advance sell, whether advance selling is optimal in continuous time, and whether excess capacity could be an optimal strategy have been addressed. Furthermore, related sensitivity analyses are performed and endpoint constraints together with alternative shapes of the service-cost function are discussed. The managerial implications of the study’s results have been demonstrated.     

广义Black-Scholes模型期权定价新方法--保险精算方法

利用公平保费原则和价格过程的实际概率测度推广了Mogens Bladt和Tina Hviid Rydberg的结果．在无中间红利和有中间红利两种情况下，把Black-Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况，在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系．给出了风险资产(股票)具有随机连续复利预期收益率和随机波动率的广义Black-Scholes模型的期权定价的一般方法．利用保险精算方法给出了股票价格遵循广义Ornstein-Uhlenback过程模型的欧式期权的精确定价公式和买权和卖权之间的平价关系．     

考虑质物耗损的银行存货质押融资决策研究

在存货需求随机波动下,为研究存货耗损对存货质押融资过程中各方决策的影响,构建由银行、中小企业和第三方物流企业(Third-Part Logistics, TPL)组成的存货质押融资系统。在考虑银行下侧风险控制和企业还贷能力下,以实现银行利润最大化为目标建立模型。分析初始耗损率、激励因子、耗损改善因子和市场需求对质押率和银行利润的影响。研究表明:(1)银行利润与质物耗损率呈负相关,银行有激励TPL提高服务水平,降低耗损率的动力。(2)银行激励TPL降低耗损率有助于银行提高质押率并拓宽质物的选择范围。(3)仅当初始耗损率超过一定限值时,银行激励带来的额外收益才会高于激励成本。最后通过数值实验进行验证,从而为银行的存货质押融资决策提供指导。     

A novel frequency-modulated differential chaotic shift keying modulation scheme based on phase separation

In frequency-modulated dierential chaos shift keying (FM-DCSK), the separation of the chaotic reference and information-bearing wavelets is performed in time domain. This separation method not only limits the attainable data rate but also demands delay components in transceiver circuits. Due to the fact that wideband radio frequency (RF) delay lines are extremely diffcult to implement with CMOS technology in ultra wideband communications, a new phase-separated FM-DCSK modulation scheme is presented in this paper to increase the data rate and to avoid the use of delay lines in both the transmitter and the receiver circuits. The feasible congurations of transmit- ter and detector are given. Besides, bit error rate (BER) performance of the proposed system is evaluated by both analysis and Monte Carlo simulations over additive white Gaussian noise (AWGN) channel.     

The role of longevity bonds in optimal portfolios

We study the optimal consumption and portfolio for an agent maximizing the expected utility of his intertemporal consumption in a financial market with: (i) a riskless asset, (ii) a stock, (iii) a bond as a derivative on the stochastic interest rate, and (iv) a longevity bond whose coupons are proportional to the population (stochastic) survival rate. With a force of mortality instantaneously uncorrelated with the interest rate (but not necessarily independent), we demonstrate that the wealth invested in the longevity bond must be taken from the ordinary bond and the riskless asset proportionally to the duration of the two bonds. This result is valid for both a complete and an incomplete financial market.     

A class of multi-period semi-variance portfolio selection with a four-factor futures price model

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Wiener process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution with parameters of the PDE is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markovitz’s portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. A hybrid genetic algorithm (GA) with particle swarm optimizer (PSO) is proposed to solve the multi-period semi-variance model. Finally, an example, which are fuel futures in Shanghai exchange market, is selected to demonstrate the effectiveness of above models and methods.     

Discrete-continuous project scheduling with discounted cash inflows and various payment models—a review of recent results

In this work discrete-continuous project scheduling problems with discounted cash flows are considered. These problems are characterized by the fact that activities of a project simultaneously require discrete and continuous resources for their execution. A class of these problems is considered, where the number of discrete resources is arbitrary, and there is one continuous, renewable resource, whose total amount available at a time is limited. Activities are non-preemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. A positive cash flow (cash inflow) is associated with each activity, and the objective is to maximize the net present value (NPV). The discrete-continuous resource-constrained project scheduling problem with discounted cash flows (DCRCPSPDCF) is defined. Four payment models are considered: lump-sum payment at the completion of the project, payments at activity completion times, payments at equal time intervals, and progress payments. Some properties of optimal schedules are proved for two important classes of processing rate functions: all functions not greater than a linear function (including linear and convex functions), and concave processing rate functions.     

需求率为斜坡型的一类变质性物品最优库存策略

本文在考虑需求率服从斜坡型分布的情况下,研究了允许缺货且缺货完全回补、变质率服从威布尔分布、补货率为无穷、有限计划期内的库存模型,证明了最优补货策略的存在性,并给出了求解最优补货策略的算法.     

The infiltration problem with constant rate in partially saturated porous media

In the present paper we study the infiltration problem with constant rate in partially saturated porous media. The main results are: (i) There exists an unique weak solution to the infiltration problem with two degenerate situations. (ii) When the infiltration rate is not large enough, the partially saturated state will fall down to completely unsaturated state with the increase of time.     

On the accelerated iterative method for estimating the optimum overrelaxation parameter

This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.     

Integrated inventory problem under trade credit in fuzzy random environment

This paper is concerned with an integrated inventory problem under trade credit where both the demand rate and deteriorating rate are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The objective of this paper is to determine the optimal inventory policy by optimizing simultaneously the replenishment cycle length and trade credit period. At first, three decision criteria are given: (1) expected value criterion, (2) chance-constrained criterion and (3) chance maximization criterion. Then, after building the fuzzy random models based on the above decision criterion, a hybrid intelligent algorithm by integrating fuzzy random simulation and genetic algorithm is employed to deal with these models. At the end, three numerical examples are given to illustrate the benefits of the models and show the effectiveness of the algorithms.     

Investors’ preference for a positive tax rate depends on the level of the interest rate

In a financial market with only one stock, Cadenillas and Pliska (Financ Stoch 3:137–165, 1999) showed that sometimes investors can take advantage of a positive tax rate to maximize their portfolio return. Buescu et al. (Math Finance 17:477–485, 2007) generalized this surprising result to a market with one stock and one bank account with zero interest rate. We consider instead a financial market with one stock and one bank account with positive interest rate. As in the papers above, we assume that there are taxes and transaction costs in the financial market. We succeed in solving the problem of an investor who wants to maximize the long-run growth rate of his investment, even though the positivity of the interest rate increases the dimensionality of the problem and the difficulty of the computations. We characterize how the investors’ preference for a positive tax rate depends on the interest rate level: investors prefer a positive tax rate when the level of the interest rate is low, and the opposite occurs when the level of the interest rate is high. Most of the contributions of C. Buescu were made during his doctoral studies at the University of Alberta. The research of C. Buescu and A. Cadenillas was supported by the Social Sciences and Humanities Research Council of Canada grants 410-2003-1401 and 410-2006-1069. We are grateful to Stanley R. Pliska for comments and suggestions to a previous version of the paper, and to the associate editor and referees for constructive remarks. Existing errors are our sole responsibility.     

Resource-constrained project scheduling with concave processing rate functions

In this paper, we address a resource-constrained project scheduling problem involving a single resource. The resource can be applied at varying consumption rates to the activities of the project. The duration of each activity is defined by a convex, non-increasing time-resource trade-off function. In addition, activities are not preemptable (ie, the resource consumption rate of an activity cannot be altered while the activity is being processed). We explicitly consider variation of the rate at which an activity is performed with variation in resource consumption rate. We designate the number of units (amount of an activity) performed per unit time with variation in resource consumption rate as the processing rate function, and assume this function to be concave. We present a tree-search-based method in concert with the solution of a nonlinear program and the use of dominance properties to determine: (i) the sequence in which to perform the activities of the project, and (ii) the resource consumption rate to allocate to each activity so as to minimize the project duration (makespan). We also present results of an experimental investigation that reveal the efficacy of the proposed methodology. Finally, we present an application of this methodology to a practical setting.     

A depletion of assets model of organizational learning*

This research investigates how population heterogeneity with respect to initial assets affects the rate of failure (or change) of organizations and social relationships. Organizations and social relationships are assumed to be endowed with initial assets which buffer against initial risks of failure. Failure is seen as the outcome of a process in which the assets are depleted and finally become exhausted. The core idea is that the assets of a unit become depleted through learning experiences which incur search costs and setbacks. Two settings are explored: A constant rate of depletion, and a declining rate of depletion of assets. The study explores additionally how the distribution of initial assets affects the failure rate of the population. It is found that the type of distribution of initial assets has a strong impact on the time dependence of the failure rate. A Normal distribution of initial assets leads to positive time dependence if the depletion rate is constant, and to negative time dependence if the depletion rate declines. The results show that population heterogeneity with respect to initial assets has effects on the time dependence of failure rates which are quite different from the popular case of population heterogeneity with respect to fit.