Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

A Generalization of the Mean Size Formula of Wavelet Packets in Lp

The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting,     

线性规划联合算法的理论与应用

本在[1]的基础上．较系统的叙述了线性规划联合算法的步骤、相关理论及其应用，指出该算法具有避免人工变量、减少迭代次数、使用灵活、应用方便等特点。     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

Implementation of a Nonzero-order Joint Transform Correlator Using Interferometric Technique

The implementation of a nonzero-order joint transform correlator using the double port Mach-Zehnder interferometric technique is proposed and demonstrated. This approach provides on-line processing for directly removing the zero-order components of a joint power spectrum in one step and performs the nonzero-order optical correlation. Experimental results are presented and discussed.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].      

Widrow-cellular neural network and optoelectronic implementation

A new type of optoelectronic cellular neural network has been developed by providing the capability of coefficients adjusment of cellular neural network (CNN) using Widrow based perceptron learning algorithm. The new supervised cellular neural network is called Widrow-CNN. Despite the unsupervised CNN, the proposed learning algorithm allows to use the Widrow-CNN for various image processing applications easily. Also, the capability of CNN for image processing and feature extraction has been improved using basic joint transform correlation architecture. This hardware application presents high speed processing capability compared to digital applications. The optoelectronic Widrow-CNN has been tested for classic CNN feature extraction problems. It yields the best results even in case of hard feature extraction problems such as diagonal line detection and vertical line determination.