A tree approach to options pricing under regime-switching jump diffusion models

A simple, efficient tree is developed to price options in a very general regime-switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime-switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.     

Insight into spontaneous recurrent calcium waves in a 3-D cardiac cell based on analysis of a 1-D deterministic model

Calcium dynamics in a cardiac cell are described by a system of 3-D non-linear stochastic partial differential equations. To obtain solutions that have biophysical properties, it is necessary to explore the model parameter space. To decrease the complexity of the parameter search, we reduce the 3-D stochastic model to a 1-D deterministic model. The reduction of the problem from 3-D to 1-D is done through an asymptotic approximation after non-dimensionalization and based on rational biophysical assumptions of the 3-D domain; the stochastic to deterministic transformation is based on the regular property of the 3-D solution. The result of the model reduction proves very effective in reducing the time required to get qualitative as well as quantitative information about parameter regions in the 3-D stochastic model including calcium dynamics (sparks, wave propagation, and recovery) observed in cardiac cells.     

Approximating of conic sections by DP curves with endpoint interpolation

Conic sections have many applications in industrial design, however, they cannot be exactly represented in polynomial form. Hence approximating conic sections with polynomials is a challenging problem. In this paper, we use the monomial form of Delgado and Peña (DP) curves and present a matrix representation for them. Using the matrix form and the least squares method, we propose a simple and efficient algorithm for approximating conic sections by DP curves of arbitrary degree with endpoint interpolation. Finally, we test and compare the proposed algorithm on some numerical examples which validates and confirms efficiency of it.     

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision‐making in unconventional emergency management. We establish an approach to online emergency decision‐making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision‐making in order to illustrate the validity of the proposed method.     

改进的无单元Galerkin方法在机场复合道面中的应用

运用改进的无单元Galerkin（Improved Element Free Galerkin,IEFG）方法计算机场复合道面的位移和应力,分析不同的节点数量和影响域比例参数对计算结果的影响.结果表明：节点数在4 000以上、影响域比例参数取2.5~3.5时计算结果较好;IEFG方法比无单元Galerkin(Element Free Galerkin,EFG)方法的精度更高,计算速度更快.计算结果可为机场道面设计提供参考.     

多项式方程区间内重根的快速判定和裁剪

目的多项式求实根问题有着广泛的应用。改进传统的裁剪方法,在多项式重根的情形下,保持计算稳定性的同时显著地提高相应的收敛阶。方法提出了基于R~3空间内的3次裁剪方法。该方法继承了传统裁剪求根方法的优点,充分利用了Bernstein基函数较好的计算稳定性,同时给出简单方法判别重根的存在性,从而使得重根的情形可以转化为单根的情形。结果与已有的基于R~1和R~2空间的3次裁剪方法相比,本文方法可以具有更好的逼近效果。单根情形下,本文方法与基于R~2空间的3次裁剪方法同时具有5次收敛阶,略高于基于R~1空间3次裁剪方法的4次收敛阶;m(≥2)重根情形下,本文方法理论上可具有5次收敛阶,明显优于已有的基于R~1和R~2空间的3次裁剪方法的4/m或5/m收敛阶。基于R~1,R~2和R~3空间的3次裁剪方法的计算时间复杂度大致相当,均为O(n~2)。结论本文方法可以快速判定重根的情形,同时具有更高的收敛阶和更好的逼近效果。     

Time Averaging Algorithms with Stopping Rules for Multi‐Agent Consensus with Noisy Measurements

A time averaging technique is introduced to consensus algorithms in networked multi‐agent systems under a noisy environment. Each agent communicates with its neighboring agents via a constant gain, while the time averaging states of the agents are considered as the values for agreement. The variation of the time averaging states then is evaluated at a specific number of iterations, where the number is given explicitly in terms of parameters related to the consensus accuracy and its probabilistic guarantee. This result establishes a rigorous stopping rule for the multi‐agent consensus with noisy measurements. Several results on this type of stopping rules are provided for undirected, directed, and time‐varying communication graphs. These theoretical results are illustrated through numerical examples.     

基于经典粗糙集的近似集动态获取方法

信息系统中的数据是动态变化的,根据动态变化的信息系统获取有用的信息,成为数据处理中的关键问题。针对该问题,分别讨论了信息系统中属性增加和减少时,近似集的动态获取方法。通过对信息系统中原有的等价类进行划分,避免了对论域的重新划分,提高了动态更新近似集的效率,通过讨论等价类与原有近似集之间的关系,给出了信息系统动获取之后的近似集与原来近似集之间的相关定理,提出了在经典粗糙集模型中,属性增减时近似集动态获取方法。实验结果验证了该方法的正确性和有效性,而且效率优于原始的方法。     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.