A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.     

Sanov meets Cramér again

We introduce a new method for proving large-deviation principles (LDPs). This method amounts to "mixing" a collection of LDPs with a sequence of probability measures that obeys itself an LDP. As an illustration, we construct from empirical measures a sequence of capacity-valued maps that can be considered as an indexed collection of LDPs. The index 1 coincides with Sanov's theorem. By taking a Poisson mixture we establish a new connection with Cramér's theorem.     

密绕载流无限长螺线管管外的磁场

对于密绕载流无限长螺线管,管外的磁场是否严格为零与管外磁场和管内磁场相比是否可以忽略不计,这是两个完全不同的问题。     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

劳动力产权界定的最优模式及其最佳路径

科斯定理并不仅仅是物权定理,更是基本人权意义上的劳动力产权定理。劳动力产权界定具有两种模式和四种路径,其中由国家以法权界定给每个劳动者,并承担起充分有效的相关保护责任,使所有劳动者成为完整意义上的法律自由人,将会成为劳动力产权界定的最优模式和最佳路径。国家合法存在的首要职能和终极理由,就是在政治学和法学意义上保护基本人权,而在经济学和管理学意义上则是保护劳动力个人自主产权。这种"个人主权和国家保护"的产权模式,对任何国家的可持续繁荣而言,都是具有普适价值的长效制度基础。     

A characterization of exact non-atomic market games

Continuous exact non-atomic games are naturally associated to certain operators between Banach spaces. It thus makes sense to study games by means of the corresponding operators. We characterize non-atomic exact market games in terms of the properties of the associated operators. We also prove a separation theorem for weak compact sets of countably additive non-atomic measures, which is of independent interest.     

The mean-variance investment problem in a constrained financial market

This paper extends the mean-variance analysis and the two-fund separation theorem to a market with some constraints, such as, the incompleteness, prohibition of short-selling, and partial information, with stochastic interest rate, and with stochastic volatility for risky assets. By maximizing a quadratic utility of terminal wealth, we show that the efficient frontier for the problem is a straight line in the mean-standard-deviation diagram. The quadratic utility function exhibits mean-variance efficiency. Our results apply to portfolios of claims in a single period, multiperiod, and continuous time.     

A note on the projection properties of Hadamard matrices obtained by the first Payley construction

We show that the projections on four factors of an arbitrary orthogonal array of strength 2 allow the estimation of main effects and two-factor interactions when all other effects are assumed to be zero, if those projections satisfy the bounds given by Weils theorem. The only exceptions are the Hadamard matrices of orders 16 and 24. A consequence is again the estimability of main effects and two-factor interactions for the projections on four factors of the first Payley construction for arbitrary run size.