限制卖空证券组合有效边缘的灵敏度分析

本文利用参数二次规划对偶性理论讨论了限制卖空的证券组合有效边缘的性质。分析的结果表明：有限制卖空的证券组合的有效边缘是一条连续的、凸的、分片二次函数连接而成的曲线。应用三元分割技术可以得到,在可选择证券空间上,有些证券从不会作为投资选择的对象。     

Modelling Sales

This paper is concerned with some aspects of direct and indirect sales rates of products, and with a model based on the sales matrix. The purpose of this consideration is to determine, through indirect sales rates, the structure of sales and to construct a model which may be used for planning and forecasting goals. In other words, by means of the sales matrix, or a model based on it, we can estimate the future sales movements. This can be done either from the assumption that past relations will be kept approximately in the same proportions, or that they will change in the future. In each case all the changes can be described through the system based on the sales matrix.     

An application of support vector machines to sales forecasting under promotions

This paper deals with sales forecasting of a given commodity in a retail store of large distribution. For many years statistical methods such as ARIMA and Exponential Smoothing have been used to this aim. However the statistical methods could fail if high irregularity of sales are present, as happens for instance in case of promotions, because they are not well suited to model the nonlinear behaviors of the sales process. In recent years new methods based on machine learning are being employed for forecasting applications. A preliminary investigation indicates that methods based on the support vector machine (SVM) are more promising than other machine learning methods for the case considered. The paper assesses the application of SVM to sales forecasting under promotion impacts, compares SVM with other statistical methods, and tackles two real case studies.     

考虑零售商销售努力的制造商入侵策略研究

渠道入侵正逐渐成为企业开拓市场,实现多渠道销售的重要策略。在考虑零售商销售努力的前提下,研究了制造商渠道入侵策略。构建了四种Stackelberg博弈模型:不入侵和无销售努力、入侵和无销售努力、不入侵和有销售努力、入侵和有销售努力。研究结果表明,线上直销渠道与线下零售渠道之间的不对称替代水平越高,越不利于制造商入侵;在制造商入侵的情况下,零售商销售努力促使制造商降低批发价格;渠道入侵成本较大且零售商销售努力投资效率高的前提下,销售努力可以有效缓解制造商入侵带来的负面影响;渠道入侵降低了零售商销售努力的动机。     

An analytic derivation of admissible efficient frontier with borrowing

The admissible efficient portfolio selection problem for risky assets has been discussed by Zhang and Nie. In this paper, the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing (money or a risk free asset) case. The admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors. The analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases: the borrowing with an upper bound constraint, or without an upper bound constraint. The influence on the admissible efficient frontier is explained under the different interest rates of the borrowing. The differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example.     

Modelling category demand in retail chains

This paper is concerned with analysis of retail-chain data on the demand of frequently bought product categories. It is intended to extend the domain of demand analysis to chain-wide data that directly concern retail managers and researchers. The proposed model explores specific structural hypotheses for chain demand and provides a comprehensive framework that admits store heterogeneity, periodic sales variation, chain-wide sales shocks, and sales dynamics. The approach is illustrated in a case study using scanner data from 10 product categories and yields empirical, quantitative insights into the structure of category demand in retail chains. The model determines category elasticities with clear implications for the effectiveness of pricing policy at the retail level and provides a useful tool for applied demand analysis in the modern retail environment.     

Optimal sales force compensation plans: an operational procedure

This paper describes an operational procedure for identifying optimal sales force compensation plans featuring salary, commissions and/or quota/bonus. Utility-maximising salespeople's behaviours and reactions to given compensation plans are simulated, and the resulting sales, costs and long-term expected profits are assessed. Then, a search technique attempts to identify the long-term profit-maximising compensation plan structure. Operationally, the simulation model parameters are calibrated so as to reflect those of an actual sales force, and consequently the optimal compensation scheme for this specific sales force can be identified. The concept is illustrated in an actual case study.     

Equilibrium in an ambiguity-averse mean–variance investors market

In a financial market composed of n risky assets and a riskless asset, where short sales are allowed and mean–variance investors can be ambiguity averse, i.e., diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets, we derive a closed form portfolio rule based on a worst case max–min criterion. Then, in a market where all investors are ambiguity-averse mean–variance investors with access to given mean return and variance–covariance estimates, we investigate conditions regarding the existence of an equilibrium price system and give an explicit formula for the equilibrium prices. In addition to the usual equilibrium properties that continue to hold in our case, we show that the diffidence of investors in a homogeneously diffident (with bounded diffidence) mean–variance investors’ market has a deflationary effect on equilibrium prices with respect to a pure mean–variance investors’ market in equilibrium. Deflationary pressure on prices may also occur if one of the investors (in an ambiguity-neutral market) with no initial short position decides to adopt an ambiguity-averse attitude. We also establish a CAPM-like property that reduces to the classical CAPM in case all investors are ambiguity-neutral.     

A single-period inventory placement problem for a supply chain with the expected profit objective

Consider the expected profit maximizing inventory placement problem in an N-stage, supply chain facing a stochastic demand for a single planning period for a specialty item with a very short selling season. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy customer demand. Stocking decisions are made before demand occurs. Because of delays, only a known fraction of demand at a stage will wait for shipments. Unsatisfied demand is lost. The revenue, salvage value, ordering, shipping, processing, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. After characterizing an optimal solution, we propose an algorithm for its computation. For the zero fixed cost case, the computations can be done on a spreadsheet given normal demands. For the nonnegative fixed cost case, we develop an effective branch and bound algorithm.     

Efficient shift scheduling in the retail sector through two-stage optimization

Efficient workforce scheduling has an important impact on store profit and customer service. Standard scheduling problems do not recognize the effect of staff availability on customer sales, however, even though the latter is an important factor in the retail sector. In this paper a two-stage model is proposed for this purpose. In the first stage a sales response model is used to specify hourly staff requirements. The output of the sales response model is then used as the input of a mixed integer optimization model, which finds an optimum assignment of the staff to daily shifts. Simulations are used to validate the sales response function, and to revise the model for more accurate results. In the simulations, customer arrivals and sales response error values are generated using appropriate distribution functions. As a case study the proposed model is applied to a Turkish retailer in the apparel sector.     

Short sales in Log-robust portfolio management

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case portfolio wealth over that set in a one-period setting. The degree of the manager’s aversion to ambiguity is incorporated through a single, intuitive parameter, which determines the size of the uncertainty set. The presence of short-selling requires the development of problem-specific techniques, because the optimization problem is not convex. In the case where assets are independent, we show that the robust optimization problem can be solved exactly as a series of linear programming problems; as a result, the approach remains tractable for large numbers of assets. We also provide insights into the structure of the optimal solution. In the case of correlated assets, we develop and test a heuristic where correlation is maintained only between assets invested in. In computational experiments, the proposed approach exhibits superior performance to that of the traditional robust approach.     

Retail replenishment models with display-space elastic demand

We study a single store multi-product inventory problem in which product sales are a composite function of shelf space. Since sales tend to deplete the amount of product on display, the effective shelf space assigned to the product diminishes with time unless replenishment occurs. We consider the problem of optimal replenishment times under these conditions. We assume a linear dependence of sales rate to effective shelf space in all our analysis. We present exact and approximate solutions for the single product and multi-product cases. For the single product case, we study the effect of space elasticity, cross elasticity and empty space elasticity on the optimal replenishment period. For the multi-product case we present a computationally attractive method using matrix exponentials and develop error bounds for this method.     

证券数增加情形下证券组合有效边缘特征灵敏度分析

本文较为详细地讨论了当证券市场不存在无风险收益证券且允许卖空时证券数的增加对 M-V证券组合有效边缘及其特征的影响 ,给出了有效边缘、渐近线斜率、全局最小方差证券组合及其协方差、最小方差证券组合的投资权数等的变化模式     

The Application of Preprocessing and Cutting Plane Techniques for a Class of Production Planning Problems

This paper investigates properties of integer programming models for a class of production planning problems. The models are developed within a decision support system to advise a sales team of the products on which to focus their efforts in gaining new orders in the short term. The products generally require processing on several manufacturing cells and involve precedence relationships. The cells are already (partially) committed with products for stock and to satisfy existing orders and therefore only the residual capacities of each cell in each time period of the planning horizon are considered. The determination of production recommendations to the sales team that make use of residual capacities is a nontrivial optimization problem. Solving such models is computationally demanding and techniques for speeding up solution times are highly desirable. An integer programming model is developed and various preprocessing techniques are investigated and evaluated. In addition, a number of cutting plane approaches have been applied. The performance of these approaches which are both general and application specific is examined.     

证券组合M-V有效前沿旋移分析的进一步研究

在市场上存在无风险资产且允许卖空的条件下,研究了新增加k种证券后对原有效前沿的影响.引入了有效证券和无效证券,给出了M-V证券组合有效前沿旋移的方向.研究结果表明新增加证券后有效前沿的斜率变大.     

摩擦市场中最优证券组合选择的极大极小法

在考虑交易成本的基础上,构造最优投资组合选择的极大极小模型,同时允许投资者卖空风险资产.在求解过程中,针对出现的非光滑函数,通过引入极大熵函数用光滑问题来逼近非光滑问题.最后推导出连续可微的方程组,可采用经典牛顿法求解.数值分析验证了该方法的有效性.     

On robust mean-variance portfolios

We derive closed-form portfolio rules for robust mean–variance portfolio optimization where the return vector is uncertain or the mean return vector is subject to estimation errors, both uncertainties being confined to an ellipsoidal uncertainty set. We consider different mean–variance formulations allowing short sales, and derive closed-form optimal portfolio rules in static and dynamic settings.     

证券数减少情形下M—V证券组合特征灵敏度分析

本文研究当市场不存在无风险收益证券且允许卖空时证券组合特征关于证券数减少的灵敏度分析,给出了有效边缘、渐近线斜率、全局最小方差证券组合及其协方差、最小方差证券组合的投资权数、最小方差证券组合之间结合线等的变化模式,得到了一些有意义的结果．这不仅是对证券组合选择理论的进一步完善,对投资者也具有一定的指导意义     

需求受库存水平影响的短生命周期物品延迟订货的库存管理

像计算机、电视机、空调等这类具有物理变质的可能性很小,但生命周期较短、不断更新换代、价值不断贬值的电子产品会发生无形变质的现象.在假设无形变质率与需求率负相关,同时在产品的存储过程中,考虑库存水平对销售量的影响情况下,研究需求受库存水平影响、且缺货时存在延迟订货的短生命周期物品的库存管理问题.创新之处在于考虑了产品的缺货问题;在允许缺货的条件下,建立了短生命周期物品的库存模型;运用数值算例进行了求解和验证;并对各参数进行了敏感性分析.     

Diversity of firm’s life cycle adapted from the firm’s technology investment decision

The stylized model presented is an optimal control model of technology investment decision of a single product firm. The firm’s technology investment does not have only a long-run positive effect but also a short-run adverse effect on its sales volume. We examine the case of high adverse investment effects where the firm finally leaves the market but we have observed different life cycles till this happens. Depending on the firm’s initial technology stock and sales volume, we compute different firm’s life cycles, which are driven by a trade-off between two strategies: technology versus sales focus strategy. Indifference curves, where managers are indifferent to apply initially technology or sales focus strategies, separate founding conditions of the firm to various classes distinguishable because of the firm’s life cycle.