THE HEX GAME THEOREM AND THE ARROW IMPOSSIBILITY THEOREM: THE CASE OF WEAK ORDERS

The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and the Brouwer fixed point theorem, and Baryshnikov showed that the impossibility theorem by Chichilnisky and the Arrow impossibility theorem are very similar. Thus, Chichilnisky and Baryshnikov are precedents for the result—linking the Arrow impossibility theorem to a fixed point theorem.     

Eisenberg's Duality in Homogeneous Programming,Shephard's Duality and Economic Analysis

This note is to reintroduce to the reader Eisenberg's symmetric duality theorem in homogeneous programming problems as a useful tool in economic analysis, and thereby to pay a due tribute to him for one of his mathematical contributions. His duality result has been almost in oblivion during the development of Shephard's duality theory between cost and production, and has seldom been mentioned in the literature about the dualities concerning Shephard's distance function, Luenberger's benefit function and directional distance functions proposed by many authors. We show that from Eisenberg's duality it is possible to derive in a systematic way these dualities so far obtained. We also present a further extension of the duality for generalized directional distance functions. In addition, we explain the relationships between the duality theorem of linear programming and that of homogeneous programming, and show how to apply the latter in those economic models in which linear programming has been utilized.     

Does the More Risk‐Averse Investor hold a Less Risky Portfolio?*

We study the suitability of using absolute risk aversion as a measure of willingness to take risk in the Arrow–Debreu portfolio framework. We define a global measure of risk for the Arrow–Debreu portfolio, which is measured by the sensitivity of an individual's Arrow–Debreu portfolio payoff to the change in the market return. We call this measure ‘conservatism’ and show that the concept of ‘more conservative’ is stronger than that of ‘more risk‐averse.’ A higher absolute risk aversion is only necessary but not sufficient to induce a less risky Arrow–Debreu portfolio. Our results not only challenge the well‐accepted notion that a more risk‐averse investor holds a less risky portfolio, but also suggest a stronger measure – conservatism – for evaluating the riskiness of portfolio.     

CHOICE OF TECHNIQUES AND THE THEOREM OF OKISHIO

This paper discusses the sufficiency of the »viability condition« of Okishio's theorem for signalling profit improving choice of techniques. Some counter-examples are given for linear technologies with joint production. Technological change which conform to the prediction of the theorem - choices made on the basis of the viability condition lead to higher average rate of profit - is called regular, and sufficient conditions for regularity are specified.     

TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.     

论消费信贷与国内需求

本文通过对消费信贷的理论与实证分析,提出了关于消费信贷与国内需求内在关系的两个定理,即长期消费需求等效定理与短期国内需求不等效定理.根据这两个定理,作者认为,消费信贷既不能拉动长期消费需求,也不能拉动短期国内需求;因此,消费信贷不应成为刺激消费的首选之策,而不断提高城乡居民的收入,才是扩大国内需求的根本举措.     

A proof of the Farkas–Minkowski theorem by a tandem method

This note presents a proof of the Farkas–Minkowski theorem. Our proof does not presuppose the closedness of a finitely generated cone, nor employs separation theorems either. Even the concept of linear independence or invertibility of matrices is not necessary. Our new device consists in proving the Farkas–Minkowski theorem and the closedness of a finitely generated cone at the same time based upon mathematical induction. We make use of a minimization problem with an equality constraint, a method familiar to economics students.     

Interest rate equalization and nonequalization by trade in Leontief-Sraffa models

A half-dozen theorems and some corollaries concerning equalization of factor prices in a time-phased Leontief-Sraffa system with steady-state profit rates are carefully stated and discussed. An example is the new Mainwaring theorem, that a 1-technique world will either have the normalized price ratio vector independent of the profit rate or uniquely determined by it. Another example is that, when intermediate goods can be imported, unchanged profit rates and changed tastes can negate the nonsubstitution theorem and alter price ratios, since now the world has more than one primary (i.e. geographical) labor.     

ANALYTICAL COMPARISONS OF OPTION PRICES IN STOCHASTIC VOLATILITY MODELS

This paper gives an ordering on option prices under various well-known martingale measures in an incomplete stochastic volatility model. Our central result is a comparison theorem that proves convex option prices are decreasing in the market price of volatility risk, the parameter governing the choice of pricing measure. The theorem is applied to order option prices under q -optimal pricing measures. In doing so, we correct orderings demonstrated numerically in Heath, Platen, and Schweizer ( Mathematical Finance , 11(4), 2001) in the special case of the Heston model.     

OVERLAPPING SETS OF PRIORS AND THE EXISTENCE OF EFFICIENT ALLOCATIONS AND EQUILIBRIA FOR RISK MEASURES

The overlapping expectations and the collective absence of arbitrage conditions introduced in the economic literature to insure existence of Pareto optima and equilibria with short‐selling when investors have a single belief about future returns, is reconsidered. Investors use measures of risk. The overlapping sets of priors and the Pareto equilibrium conditions introduced by Heath and Ku for coherent risk measures are respectively reinterpreted as a weak no‐arbitrage and a weak collective absence of arbitrage conditions and shown to imply existence of Pareto optima and Arrow–Debreu equilibria.     

THE FREQUENCY OF QUANTITY SURCHARGES: REPLICATION AND EXTENSION

Widrick's research has established that larger sizes of grocery products are not always less expensive per unit than smaller sizes, or that quantity surcharges exist. The purpose of this research was to validate and extend Widrick's work. In this research, the overall incidence of quantity surcharges was 18.6%. Surcharges were found to occur more often when numerous brand sizes were offered and non-integer package size comparisons were required. Additionally, personal care products, not previously included in quantity surcharge research, were found to have a lower incidence of surcharges than food and laundry products. The research indicates there may be possible payoffs to consumers who make unit price comparisons rather than employing the economy size rule.     

The Harris-Todaro hypothesis and the Heckscher-Ohlin-Samuelson trade model : A synthesis

We report a model of the Harris-Todaro variety in which capital is mobile and the urban wage is endogenous. Our model subsumes several other models presented in the literature. We extend the central theorems of trade to our model and also present formulae for the shadow wage and shadow rental. Our principal findings include (a) nonexistence of equilibrium in an important specialization of the model; (b) a factor-price and unemployment rate equalization theorem: and (c) an identical subsidy to labor but a differential subsidy to capital for obtaining a second-best optimum.     

ON A GENERALIZED VON NEUMANN MODEL

The main aim of the paper is to give a constructive proof to an existence theorem concerning the generalized von Neumann model à la Morishima in a particular case which arises by dropping and replacing a strong continuity assumption of Morishima, whose existence theorem does not work (as the appendix example shows) when all of Morishima's other assumptions but that continuity assumption hold. In particular, the paper proves that the generalized von Neumann model à la Morishima has a solution when all people consume the same commodities in the same proportions, with a substitution effect equal to zero, even if some commodities are never consumed and not all processes require labour. Moreover, it shows a way to construct a solution by solving a Linear Complementarity Problem with Lemke's complementarity pivot algorithm.     

A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM

We propose a Fundamental Theorem of Asset Pricing and a Super‐Replication Theorem in a model‐independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a superlinearly growing payoff‐function, e.g., a power option. This condition is not needed when sufficiently many vanilla options maturing at the horizon T are traded in the market.     

Variable returns to scale in general equilibrium theory once again

This paper relaxes some assumptions made by Jones (1968) and reconsiders the implications of variable returns to scale (VRS) for the Stolper-Samuelson and Rybczynski theorems. It also analyses for the first time the relationship between factor-returns and factor-supplies at constant commodity-prices. It is shown that the validity of the Rybczynski and/or Stolper-Samuelson theorem is neither necessary nor sufficient for the production possibilities frontier to be locally strictly concave to the origin. Several other new results are derived and an attempt is made to give an intuitive explanation of the most important findings.     

Empirical tests of canonical nonparametric American option‐pricing methods

Alcock and Carmichael (2008, The Journal of Futures Markets, 28, 717–748) introduce a nonparametric method for pricing American‐style options, that is derived from the canonical valuation developed by Stutzer (1996, The Journal of Finance, 51, 1633–1652). Although the statistical properties of this nonparametric pricing methodology have been studied in a controlled simulation environment, no study has yet examined the empirical validity of this method. We introduce an extension to this method that incorporates information contained in a small number of observed option prices. We explore the applicability of both the original method and our extension using a large sample of OEX American index options traded on the S&P100 index. Although the Alcock and Carmichael method fails to outperform a traditional implied‐volatility‐based Black–Scholes valuation or a binomial tree approach, our extension generates significantly lower pricing errors and performs comparably well to the implied‐volatility Black–Scholes pricing, in particular for out‐of‐the‐money American put options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:509–532, 2010     

COMONOTONIC MEASURES OF MULTIVARIATE RISKS

We propose a multivariate extension of a well‐known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invariance, subadditivity, and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.     

基于模糊偏序关系的员工互评方法

在绩效考评中应当重视员工互评的重要性,利用模糊偏序关系的排序方法,来解决绩效考评中员工互评的心理测度的模糊性问题,论证了用模糊偏序关系对心理测度进行排序是一种较好的方法,并用实例验证该方法对员工互评的可行性。     

Drivers of Brand Extension Success: What Really Matters for Luxury Brands

The use of brand extensions has become fundamental to the business model of most luxury brands. Many traditional luxury brands such as Louis Vuitton or Chanel have expanded into traditional luxury sectors beyond their core business. Some brands such as Armani or Prada even crossed boundaries to nontraditional lifestyle segments to pursue new business opportunities. Given the high practical relevance of brand extensions for luxury brands and the importance to understand the success factors for their extendibility and potential backward effects on the parent brand, surprisingly little research has addressed these issues for luxury brands in comparison to nonluxury brands. The current research reveals extension‐related differences between luxury and nonluxury brands by simultaneously analyzing key dimensions of parent brand value, fit, and extension category involvement on the consumer's attitude toward the brand extension, which in turn influences the postextension image of the parent brand. Results of a structural equation model based on a survey among 492 participants show that the predominant driver of brand extension success for both luxury and nonluxury brands is overall extension fit, followed by the consumer's involvement in the extension category. The influence of functional value of the parent brand on the extension evaluation is more important for nonluxury brands. The hedonic value of the parent brand is found to be of relevance only in case of luxury brands. Moreover, a reciprocal spillover effect between the extension evaluation and the parent brand evaluation is observed. The degree of luxuriousness of the parent brand moderates this relationship. This effect is weaker for luxury brands.