ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

交易成本、禀赋效应与国有股权转让定价——兼论国有企业混合所有制改革的新思路

国有企业混合所有制改革是积极发展混合所有制经济的关键,完善的定价机制有助于推进国有企业混合所有制改革。国有股转让过程中存在大量的交易成本,扭曲了定价体系。基于科斯定理,可以发现,明晰产权是优化定价体系有效途径。但是,禀赋效应的存在,使得科斯定理无法完全解决国有股转让定价问题。对此,需要采取市场和非市场的政策组合,以此来完善国有股转让定价机制,推进国有企业混合所有制改革。     

The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time

We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's modeling of foreign exchange markets under transaction costs. The financial market is described by a   d × d   matrix-valued stochastic process  (Π _t ) ^T _{t =0}  specifying the mutual bid and ask prices between d assets. We introduce the notion of "robust no arbitrage," which is a version of the no-arbitrage concept, robust with respect to small changes of the bid-ask spreads of  (Π _t ) ^T _{t =0}  . The main theorem states that the bid-ask process  (Π _t ) ^T _{t =0}  satisfies the robust no-arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Kabanov-Stricker pertaining to the case of finite Ω, as well as the theorem of Dalang, Morton, and Willinger and Kabanov, Rásonyi, and Stricker, pertaining to the case of general Ω. An example of a  5 × 5  -dimensional process  (Π _t )² _{t =0}  shows that, in this theorem, the robust no-arbitrage condition cannot be replaced by the so-called strict no-arbitrage condition, thus answering negatively a question raised by Kabanov, Rásonyi, and Stricker.     

关于风险投资内在机理的经济学分析

从经济学的角度对风险投资进行了内部和外部两个方面的具体分析。根据交易成本理论和信息不对称理论分析了风险投资的特点 ,揭示了风险投资迅速发展的内在机理 ;依据科斯定理和“囚徒困境”模型 ,阐明了政府积极参与的必要性     

享年次高的诺贝尔奖得主——新制度经济学大师罗纳德·科斯

1991年诺贝尔经济学奖得主、英国和美国(双重国籍)经济学家和法学家罗纳德·科斯是交易成本理论、科斯定理和科斯猜想的首创者,法律经济学和新制度经济学的开山鼻祖,产权理论和产权经济学的奠基人,他开启了产权理论、法律经济学和新制度经济学三个领域的研究方向。科斯是国际经济学界的泰斗级大师和巨匠,他在阐述经济组织产生的原理、交易成本分析以及推动法学、经济史和组织理论的发展方面作出重要贡献,发展了新古典经济学,开创了现代企业理论。科斯一生都关切和热爱中国,一直密切关注着中国的经济改革,其经济理论和深邃思想对中国的经济改革影响巨大而深远。     

An alternative proof of the nonemptiness of the private core

Summary. We focus on the private core [19] of an economy with a finite number of agents with differential information, a continuum of states and an infinite number of commodities. We state a nonemptiness result for the private core and provide a proof based on a fixed-point argument. Received: October 4, 1999; revised version: June 7, 2000     

一类泛函脉冲微分方程周期正解的存在性

利用Krasnoselskii不动点定理,讨论一类带参数的泛函脉冲微分方程多个周期正解存在的充分条件,在f(x)和I_k(x) 均为非超线性和非次线性的条件下,得到该类微分方程多个周期正解存在的一些新结果。     

The Generalized Composite Commodity Theorem and Food Demand Estimation

This article reports tests of aggregation over consumer food products and estimates of aggregate food demand elasticities. Evidence that food demand variables follow unit root processes leads us to build on and simplify existing tests of the Generalized Composite Commodity Theorem. We compute food demand elasticities using a method of cointegration that is shown to apply to a convenient but nonlinear functional form. Estimates are based on consumer reported expenditure data rather than commercial disappearance data.     

积分第一中值定理的证明与推广

本文根据积分上限函数的性质利用微分中值定理证明了积分第一中值定理,用改进的介值定理证明了ξ∈(a,b),并推广了积分第一中值定理。     

Factor substitution and factor intensities in models with more factors than goods

This paper considers the commodity prices–factor prices relation in models with more factors than consumption goods. Under some simple factor substitutability assumptions, many results in the   n  ×  n   cases have counterparts in the   l  ×  n   cases. The proportional price changes of the "middle factors" will be trapped between those of the "extreme factors". A weak and a strong Stolper–Samuelson theorem can also be proven. If the numbers of goods and perfectly complementary factors are equal and the production functions have the nested constant elasticity of substitution form, two of the complementary factors would have the most extreme relative price changes, regardless of the factor intensities.