The geometry of relative arbitrage

Consider an equity market with n stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function that assigns a portfolio vector to each possible value of the market weight, and we perform self-financing trading using this portfolio function. We study the problem of characterizing functions such that the resulting portfolio will outperform the market portfolio in the long run under the conditions of diversity and sufficient volatility. No other assumption on the future behavior of stock prices is made. We prove that the only solutions are functionally generated portfolios in the sense of Fernholz. A second characterization is given as the optimal maps of a remarkable optimal transport problem. Both characterizations follow from a novel property of portfolios called multiplicative cyclical monotonicity.     

Long-time behaviour of soliton ensembles. Part I––Emergence of ensembles

This paper is focused on the emergence of the KdV solitons from an initial harmonic excitation. In the long run this process is characterized not so much by regular soliton trains but rather by soliton ensembles. It has been shown explicitly that under indicated initial conditions the width of emerging solitons are mostly larger than the distance between maxima of wave profiles. Consequently, visible are the ensembles formed by several simultaneously interacting solitons including also hidden (virtual) solitons. The conditions for emerging such ensembles are studied over the wide range of amplitude ratios for typical dispersion parameters. Based on that analysis, it is possible to cast more light to the recurrence and periodicity in the long run (see Part II).     

Learning dynamic prices in electronic retail markets with customer segmentation

In this paper, we use reinforcement learning (RL) techniques to determine dynamic prices in an electronic monopolistic retail market. The market that we consider consists of two natural segments of customers, captives and shoppers. Captives are mature, loyal buyers whereas the shoppers are more price sensitive and are attracted by sales promotions and volume discounts. The seller is the learning agent in the system and uses RL to learn from the environment. Under (reasonable) assumptions about the arrival process of customers, inventory replenishment policy, and replenishment lead time distribution, the system becomes a Markov decision process thus enabling the use of a wide spectrum of learning algorithms. In this paper, we use the Q-learning algorithm for RL to arrive at optimal dynamic prices that optimize the seller’s performance metric (either long term discounted profit or long run average profit per unit time). Our model and methodology can also be used to compute optimal reorder quantity and optimal reorder point for the inventory policy followed by the seller and to compute the optimal volume discounts to be offered to the shoppers.     

Personnel Recruitment Policies and Long-Term Production Planning

Any organization or industry operating in a market where there is unmet demand will be under considerable pressure to meet the demand as quickly as possible. This short-term objective can be met by rapidly expanding productive capacity in terms of both plant or other equipment and also manpower. If the commodity in demand is durable—e.g. housing, cars, computers—then when the initial requirement is met, further output is for replacement purposes. Production during the expansion phase, planned to eliminate the backlog of demand may be much greater than that needed for the next phase, meeting recurrent replacement demand. If capacity is allowed to run down, a later increase in demand will possibly find the organization with too little capacity. There follows a potentially continuing cycle of under- and over-production. Since manpower comprises a significant part of the capacity, this creates a possible cycle of under- and over-employment.Mathematical models of manpower systems can be adapted to investigate the consequences of controlling recruitment policies over fairly long periods of time. If costs can be ascribed to both under- and over-production it is possible to combine the manpower models with mathematical programming techniques to produce optimal longterm recruitment policies.The possible development of the telephone network in the Republic of Ireland is used as an illustrative example. Here it has already been established by government operational research scientists that meeting the original target number of installations for the early 1980's would require impossibly large levels of recruitment immediately. Our model shows that, if the target were achieved, an intolerably large proportion of the workforce would be redundant in a few years time. We use a linear programming model to illustrate viable policies trading off present delays in satisfying demand against future overmanning.     

基于ROI,VMI和CS三种库存方式长短期绩效的对比研究

ROI、VMI和Cs是基于供应链的三种库存管理方式.本文以两层供应链的ROI、VMI和CS方式为例,通过数学模型和具体算例,比较分析了三种库存方式下买方和卖方成本和利润构成的不同之处.本文研究发现:在长期内相对于ROI方式而言,VMI方式下供应链的效率更高;如果卖方的单位存储成本大于买方,CS方式下供应链的长短期效率可能高于VMI更高于ROI方式.     

Oligopoly and stability

In this paper, the so called Theocharis–Cournot problem is reconsidered. It concerns the relation between oligopoly and perfect competition, in particular the destabilization of Cournot equilibrium when the number of competitors increases. Using a CES production function where one input, capital, is fixed during periods of investment, a mixed short/long run market dynamics is set up. In the short run, with capital fixed, there is a capacity limit for production possibilities, whereas, at moments of capital renewal there are constant returns to scale. In this setting the local stability of Cournot equilibrium is reconsidered. It is demonstrated that if no more than two firms reinvest in the same time period, and the wage rate is not too high, then the Cournot equilibrium is stable.     

Market Price Calculations in Restructured Electricity Markets

In the traditional organisation of the power market, the generation Unit Commitment and Dispatch problem was solved as a cost minimisation problem. After deregulation of the electricity sector, the problem must be solved as a profit maximising problem. It is necessary to find feasible market prices. This is difficult, because simple marginal cost based prices not always cover startup and operation-independent costs, with the result that the generator would choose not to run with such prices. In this paper a market structure is proposed with a central market operator computing the market equilibrium for both energy and reserves, based on generator offers and consumer bids. It is shown that it is possible to find feasible market prices. Using a simple test system, it is shown that demand elasticity can have a profound impact on prices and generator revenues and profits during peaking hours.     

Some bounds for Markov chains

In principle it is possible to characterize the long run behavior of any evolutionary game by finding an analytical expression for its limit probability distribution. However, it is cumbersome to do so when the state space is large and the rate of mutation is significant. This paper gives upper and lower bounds for the limit distribution, which are easy to compute. The bounds are expressed in terms of the maximal and minimal row sums of parts of the transition matrix.     

齐次生产函数条件下长期成本函数的确定方法

文章研究一般性齐次生产函数条件下长期成本函数的确定方法，证明了长期成本函数是关于产量的幂函数，并指出了长期边际成本函数和长期平均成本函数之间的特殊关系。     

中国地震保险市场的演化博弈均衡——政府预防性补贴和救济性给付分析

我国应对地震风险的资金安排可以按事前与事后划分为灾前预防性质和灾后给付性质。在非预期预算一定的情况下,政府应如何分配救灾基金？对地震保险市场均衡影响如何？本文构建了一个三方演化博弈模型,分析发现政府适度的灾后救济能够同时保证效率与公平,而过度的灾后救济会在长期提高居民的救灾预期,抑制商业地震保险市场的形成与完善。同时,引导与改善社会风险管理意识和风险感知也是提高地震保险市场效率的关键。     

A cobweb model with gradient adjustment mechanism: nonlinear dynamics and multistability

A cobweb model, characterized by boundedly rational producers with a production adjustment mechanism based on the gradient rule, is described by a nonlinear discrete time dynamical system of the plane. Firms do not have a complete knowledge of the demand function and try to infer how the market will respond to their production changes by an empirical estimates of the marginal profits. Analytical conditions for local stability of the market equilibrium are provided, showing that the stability loss of the market equilibrium may give rise to chaotic dynamic as well. When memory is introduced in the production adjustment mechanism, a locally stabilizing effect is revealed as well as a globally qualitatively destabilizing role for memory. This is related to the occurrence of period doubling and Neimark–Sacker bifurcations, the latter being of supercritical nature as analytically proved. Endogenous fluctuations and multistability, with consequent loss of predictability in the long run dynamics, are observed.     

国内外期铜价格之间的长期记忆成分和短期波动溢出效应

本文区分国内外期铜市场价格的长记忆成分和短期波动溢出效应,采用信息共享模型和永久一瞬时模型分离出不同期铜市场价格间的长记忆成分,得到不同市场期铜价格对"隐含有效价格"的贡献度;而且,利用t分布的BEKK模型分析两个市场期铜价格的短期波动溢出.特别,我们在BEKK基础上定义了不同变量间的波动溢出项,对两个市场期铜价格的波动溢出进行了度量.根据测算结果,我们发现国内外期铜价格有着紧密的联系,无论在长期,还是在短期,国外市场期铜价格的影响力都较大.     

Asymptotic arbitrage and large deviations

Typical models of mathematical finance admit equivalent martingale measures up to any finite time horizon but not globally, and this means that arbitrage opportunities arise in the long run. In this paper, we derive explicit estimates for asymptotic arbitrage, and we show how they are related to large deviation estimates for the market price of risk. As a case study we consider a geometric Ornstein–Uhlenbeck process. In this setting we also compute the optimal trading strategies and the resulting optimal growth rates of expected utility for all HARA utilities.     

基于演化博弈的发电侧电力市场长期均衡模型

研究包含生产同质电力产品的两组 (种群 )企业——低成本发电企业和高成本发电企业的发电侧电力市场的长期均衡问题 .应用演化博弈论的有限种群演化稳定战略概念 ,证明了有限种群的演化稳定战略产量分别等于两组 (种群 )企业的竞争产量 .通过建立基于企业战略模仿和试验的随机演化模型 ,分析了发电侧电力市场长期均衡的演化过程 .     

Sustaining long-term supply chain partnerships using price-only contracts

In this paper, we study how an informal, long-term relationship between a manufacturer and a retailer performs in turbulent market environments characterized by uncertain demand. We show that the long-term partnership based on repeated interaction is sustainable under price-only contracts when the supply chain partners are sufficiently patient. That is, the channel can be coordinated over a long time horizon when the factor whereby the members discount the future value of this trusting relationship is sufficiently high. Second, above the minimum discount factor, a range of wholesale prices exists that can sustain the long-term partnership, and there are different possible profit divisions between the two players. Third, when the market is turbulent, i.e., either the expected demand or the demand variance changes from period to period according to a probabilistic law, it is typically less possible to sustain the long-term partnership in a booming market or in a market with low demand variability. Finally, obtaining more information about future market fluctuation may not help the supply chain to sustain the long-term partnership, due to partners’ strategic considerations. With the availability of the market signal, total supply chain profits increase, but the retailer may even be worse-off.     

How Many Distribution Channels?

An investigation was made into the relationship between market share and the number of distribution channels used by an individual manufacturer in a particular area. A probabilistic gravity model was employed to explore this relationship. A simulation approach was used to run the model. Parameter values were randomly selected at run time and replications made for each level on the independent variable, the number of distribution channels. This simulation approach is fundamentally different from the usual approach of determining specific parameter values through empirical model fitting procedures.     

TIMBER SUPPLY UNDER DEMAND UNCERTAINTY: WELFARE GAINS FROM PERFECT COMPETITION WITH RATIONAL EXPECTATIONS

ABSTRACT. This paper presents a noneconometric approach to estimating the short‐run timber supply function based on optimal harvest decisions. Determination of optimal harvest levels and estimation of supply function coefficients are integrated into one step by incorporating a parametric short‐run timber supply function into the harvest decision model. In this manner we convert the original harvest decision model into a new optimization problem with the supply function coefficients functioning as “decision variables.” Optimal solution to the new decision model gives the coefficients of the short‐run supply function and, indirectly, the optimal harvest levels. This approach enables us to develop stochastic models of the timber market that are particularly useful for forest sector analysis involving comparison of alternative institutional regimes or policy proposals and when the timber market is affected by stochastic variables. For demonstration purposes, we apply this method to compare the performances of two timber market regimes (perfect competition and monopoly) under demand uncertainty, using the Swedish data. The results show that the expected timber price is 22 percent lower and the expected annual timber supply is 43 percent higher in the competitive market than in the monopoly market. This confirms the theoretical result that monopoly reduces supply and increases price. The expected social welfare gain from perfect competition over monopoly is about 24 percent.     

Dynamic investment strategies with demand-side and cost-side risks

Investments in cost reductions are critical for the long run success of companies that operate in dynamic and stochastic market environments. This paper studies optimal investment in cost reductions as a real option under the assumption that a single firm faces two different sources of risk, stochastic demand and input prices. We derive optimal investment strategies for a monopoly as well as a firm in a perfectly competitive market and show that in case of high marginal costs, cost reductions take place earlier in competitive than in monopoly markets. While the existence of an option to invest in cost reductions increases firm value it also increases a firm’s systematic risk. Risk can be smaller in a monopolistic than in a competitive industry.     

A jump model for fads in asset prices under asymmetric information

This paper addresses how asymmetric information, fads and Lévy jumps in the price of an asset affect the optimal portfolio strategies and maximum expected utilities of two distinct classes of rational investors in a financial market. We obtain the investors’ optimal portfolios and maximum expected logarithmic utilities and show that the optimal portfolio of each investor is more or less than its Merton optimal. Our approximation results suggest that jumps reduce the excess asymptotic utility of the informed investor relative to that of uninformed investor, and hence jump risk could be helpful for market efficiency as an indirect reducer of information asymmetry. Our study also suggests that investors should pay more attention to the overall variance of the asset pricing process when jumps exist in fads models. Moreover, if there are very little or too much fads, then the informed investor has no utility advantage in the long run.     

Evaluating the profitability of advertising for heavily advertised brands: an empirical study

Even companies with large advertising budgets are sceptical of OR models in advertising—such models often appear overly complex, unrealistic and costly to use. Here a simple econometric model is proposed which utilises existing company data. The parameters are estimated for the five leading brands in a sector of the German alcoholic drinks market. Estimates of the short and long run advertising elasticities are made and optimum advertising appropriations are calculated.