Extending pricing rules with general risk functions

The paper addresses pricing issues in imperfect and/or incomplete markets if the risk level of the hedging strategy is measured by a general risk function. Convex Optimization Theory is used in order to extend pricing rules for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Necessary and sufficient optimality conditions are provided in a very general setting. For imperfect markets the extended pricing rules reduce the bid-ask spread. The findings are particularized so as to study with more detail some concrete examples, including the Conditional Value at Risk and some properties of the Standard Deviation. Applications dealing with the valuation of volatility linked derivatives are discussed.     

Borderline vs. unknown: comparing three-valued representations of imperfect information

In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-Rodríguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions.     

Dynamic consistency in incomplete information games under ambiguity

We develop a general framework of incomplete information games under ambiguity which extends the traditional framework of Bayesian games to the context of Ellsberg-type ambiguity. We then propose new solution concepts called ex ante and interim Γ-maximin equilibrium for solving such games. We show that, unlike the standard notion of Bayesian Nash equilibrium, these concepts may lead to rather different recommendations for the same game under ambiguity. This phenomenon is often referred to as dynamic inconsistency. Moreover, we characterize the sufficient condition under which dynamic consistency is assured in this generalized framework.     

Resolvable group divisible designs with block size four and index three

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hⁿ and index three. The necessary conditions for the existence of such a design are n?4 and hn≡0. These necessary conditions are shown to be sufficient except for (h,n)∈{(2,4),(2,6)} and possibly excepting (h,n)=(2,54).     

The effect of initial spatial correlations on late time kinetics of bimolecular irreversible reactions

We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional dispersion equation. As has been previously shown, we demonstrate that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We do so in a fully analytical manner using moment equations. In particular the novel aspect of this work is that we focus on the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. We focus on short range and long (power law) range correlations and demonstrate how long range correlations can give rise to different late time scalings than one would expect purely from the underlying transport model. For the short range correlations the late time scalings deviate from the well mixed t⁻¹$t^{-1}$ and scale like t^−1/2α$t^{-1/2\alpha }$, where 1<α≤2$1<\alpha \le 2$ is the fractional dispersion exponent, in agreement with previous studies. For the long range correlation case it scales like t^−β/2α$t^{-\beta /2\alpha }$, where 0<β<1$0<\beta <1$ is the power law correlation exponent.     

The game for the speed of convergence in repeated games of incomplete information

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value v _∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to v _∞ (p) (and will converge from above to v _∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payoffs-to the value v _∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG _∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v _n (p)− v _∞ (p) is of the order of magnitude of . In that case the value of SG _∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛^∞={X _k }^∞ _k=1, one defines for each n : V _n (𝔛^∞) ≔E∑ⁿ _k=1 |X _k+1 − X _k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛^∞, V _n (𝔛^∞) can be of the order of magnitude of n ^1/2−ε, for arbitrarily small ε>0. Received January 1999/Final version April 2002     

American Options Exercise Boundary When the Volatility Changes Randomly

The American put option exercise boundary has been studied extensively as a function of time and the underlying asset price. In this paper we analyze its dependence on the volatility, since the Black and Scholes model is used in practice via the (varying) implied volatility parameter. We consider a stochastic volatility model for the underlying asset price. We provide an extension of the regularity results of the American put option price function and we prove that the optimal exercise boundary is a decreasing function of the current volatility process realization. Accepted 13 January 1998     

Run orders and quantitative factors in asymmetrical designs

Results on run orders leading to trend-free symmetrical factorial designs are extended to the asymmetrical case, using the character theory of abelian groups. The tools developed apply equally to the construction of designs for quantitative treatment factors with eight or more regularly spaced levels. Abelian group theory can also be used to find minimum-cost run orders for asymmetrical designs, with a cost based on the number of changes of levels between successive runs.     

SYNTHESIS AND STRUCTURAL CHARACTERIZATION OF IN-COMPLETE CUBANE CLUSTER C(MoCu_3S_3) (O)(μ-dtp)(PPh_3)_3]

<正> A new mixed-metal sulfido incomplete cubane cluster [(MoCuS3) (O) (μ-dtp) (PPh3)3] Cdtp = S2P (OC2H5)2] has been prepared by reaction of (NH4)2MoOS3 with Cu(dtp) (PPh3)2 in dimethylformamide solution. It crystallizes in the triclinic space group P1, a = 13.810(5), b = 19. 753(5), c=11. 719(4) A. α=99. 42(2), β=107. 24(3),γ=88. 05(3)°, V = 3012(2)A3, Dc = l. 51g/cm3and Z = 2. Final R=0. 046, Rw = 0. 056 for 7700 unique intensity data(I≥3σ(I)). The central unit [MoCu3S3]3+ can be described as a distorted incomplete cube with one missing corner. The Mo atom is tetrahedrally coordinated by three μ3-S atoms and one terminal O atom. Two Cu atoms are tetrahedrally coordinated whereas the third Cu atom has a highly distorted trigonal environment. The mean Mo - Cu bond length is 2. 752A. The Cu...Cu distances are in the range of 3. 200(1) -3. 740(1) A which are too long to form bonds.     

基于顺序注射分析的海水亚硝酸盐快速检测方法研究

为实现海水亚硝酸盐的快速检测,使测量过程更适用于在线监测,对前期已有的顺序注射分析技术进行了优化,结合自主研制的Z型高灵敏度液芯波导样品池和多适应环管器,基于分光光度检测方法,在不完全显色反应的基础上,建立了一种海水亚硝酸盐快速全自动检测方法。进样技术中高精度注射泵与多通道选择阀配合,顺序吸入样品和试剂至储液盘管后,再反推至混合盘管,期间发生不完全显色反应,并最终由注射泵将显色混合溶液缓推过Z型液芯波导样品池,同步流动检测溶液吸光度变化,结合朗伯比尔定律最终获取待测亚硝酸盐溶液浓度。为达到稳定且快速分析的目的,分析了测量方法中几个关键参数,如不完全显色反应时间、检测时流速和盐度对测量结果的影响,寻求最佳的技术及参数组合。不完全显色反应研究结果表明,在10~60 s显色时间范围内,吸光度检测结果的相对标准误差（RSD）均不超过1.64%,说明10~60 s的显色时间对本方法无影响,因此选择10s作为快速检测方法的显色反应时间。通过对不同流速情况下样品检测结果的分析发现,流速过快会导致检测不稳定,过慢则不利于快速分析,选择吸光度测量较为稳定的10,11.6,13和15 μL·s-1四个流速,对测量结果的稳定性和重复性进行分析,结果表明,上述四个流速下的线性效果都很好,因此,选择最快的15 μL·s-1作为该方法的检测流速。为验证该方法对盐度的敏感性,以适应淡水和大范围海水为出发点,研究分析了0~35盐度范围内,三种不同浓度（150,250,350 μg·L-1）亚硝酸盐溶液的吸光度变化情况,得到的RSD分别为1.39%,2.03%和1.28%,证明盐度对本方法的吸光度测量基本无影响。对80,150和250 μg·L-1亚硝酸盐标准溶液平行测定11次得到的RSD分别为2.13%,1.07%和1.83%,说明本方法精密度较好。通过对空白样品进行10次平行样测量,计算得到本方法检出限为37 μg·L-1（约0.5 μmol·L-1）。为验证本方法的可信度,利用该快速检测方法和《海洋调查规范》标准测量方法对同一批次亚硝酸盐标准溶液制作标准曲线,二者的R2均大于0.999,对同一浓度样品两种方法得到的测量结果数据拟合线性回归方程为y=1.046 1x-0.005 7,R2=0.999 6,说明两种检测方法结果高度一致,更进一步验证了该研究快速测量方法的可行性和可靠性。亚硝酸盐快速检测方法测样速率高达50样·h-1,与传统的人工检测和流动注射分析方法相比,亚硝酸盐的测量耗时从十几分钟缩短到1 min左右,检测分析过程中样品和试剂消耗量极少,测量过程重复性好,整个测量过程全自动进行,操作更为简单智能,避免了人工介入带来的误差,使得基于分光光度的营养盐要素在线及原位检测系统更加小巧、快速和低耗,更适用于现场在线及长时间序列监测,具有很广的应用范围和较好的应用前景。