Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models

This work provides a Markov-modulated stochastic approximation based approach for pricing American put options under a regime-switching geometric Brownian motion market model. The solutions of pricing American options may be characterized by certain threshold values. Here, a class of Markov-modulated stochastic approximation (SA) algorithms is developed to determine the optimal threshold levels. For option pricing in a finite horizon, a SA procedure is carried out for a fixed time T. As T varies, the optimal threshold values obtained via SA trace out a curve, called the threshold frontier. Numerical experiments are reported to demonstrate the effectiveness of the approach. Our approach provides us with a viable computational tool and has advantage in terms of the reduced computational complexity compared with the variational or quasivariational inequality methods for optimal stopping.Communicated by C. T. LeondesThis research was supported in part by the National Science Foundation under Grant DMS-0304928, and in part by the National Natural Science Foundation of China under Grant 60574069.     

A general framework for cooperation under uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the associated cooperative games are totally balanced. Finally, we consider several example situations.     

Wick型Clannish Random Walker’s Parabolic方程的精确解

通过白噪声泛函分析理论、Hermite变换和广义F展开法，分别得到Wick型clannish random walker’s parabolic方程和变系数的clannish walker’s parabolic方程的白噪声泛函解、三角函数解及双曲函数解．     

Asymptotic expansions of the Robbins-Monro process

Assume that the function values f(x) of an unknown regression function f: ℝ → ℝ can be observed with some random error V. To estimate the zero ϑ of f, Robbins and Monro suggested to run the recursion X _n+1 = X _n − a/n Y _n with Y _n = f(X _n ) − V _n . Under regularity assumptions, the normalized Robbins-Monro process, given by (X _n+1 − ϑ)/√Var(X _n+1, is asymptotically standard normal. In this paper Edgeworth expansions are presented which provide approximations of the distribution function up to an error of order o(1/√n) or even o(1/n). As corollaries asymptotic confidence intervals for the unknown parameter ϑ are obtained with coverage probability errors of order O(1/n). Further results concern Cornish-Fisher expansions of the quantile function, an Edgeworth correction of the distribution function and a stochastic expansion in terms of a bivariate polynomial in 1/√n and a standard normal random variable. The proofs of this paper heavily rely on recently published results on Edgeworth expansions for approximations of the Robbins-Monro process.      

在周期激励及噪声干扰下双稳系统性态的数值模拟研究

本文利用ＭｏｎｔｅＣａｒｌｏ方法（ＭＣＭ），对周期激励及噪声干扰作用下双稳系统的性态进行研究．获得了系统周期形式的非平稳概率分布及位移──速度联合分布．发现它们与系统势能的某些拓扑关系．本文对跳跃和信号强度随参数变化的关系也进行了探讨．     

取代基对卟啉三阶光学非线性及弛豫过程的影响

研究了取代基对卟啉三阶光学非线性和激发态弛豫过程的影响，发现在同一取代位置，推电子基团取代使得卟啉三阶光学非线性极化纱数Ｘ值相对影响，而吸电子基团取代使得卟啉Ｘ值相对减少，对同一取代基在不同取代装置，发现推电子基团在邻位取代的Ｘ值大于其在对位取代卟啉的Ｘ值，而吸电子基团在邻位取代的Ｘ值小于其在对位取代卟啉的Ｘ值，另外，还发现推电子基团取代的卟啉弛豫过程比吸电子基团取代的卟啉弛豫过程快７倍。     

Energy relaxation method for chemical non‐equilibrium flow computations

In this paper, an algorithm for chemical non‐equilibrium hypersonic flow is developed based on the concept of energy relaxation method (ERM). The new system of equations obtained are studied using finite volume method with Harten–Lax–van Leer scheme for contact (HLLC). The original HLLC method is modified here to account for additional species and split energy equations. Higher order spatial accuracy is achieved using MUSCL reconstruction of the flow variables with van Albada limiter. The thermal equilibrium is considered for the analysis and the species data are generated using polynomial correlations. The single temperature model of Dunn and Kang is used for chemical relaxation. The computed results for a flow field over a hemispherical cylinder at Mach number of 16.34 obtained using the present solver are found to be promising and computationally (25%) more efficient. The present solver captures physically correct solution as the entropy conditions are satisfied automatically during the computations. Copyright © 2007 John Wiley & Sons, Ltd.     

Substitutional adsorption of K on Fe(100)

The adsorption of potassium on Fe(100) was studied by time-of-flight forward scattering and recoiling spectroscopy (TOF-SARS), low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). After heating to 650 K of the potassium saturated surface the formation of a p(3 × 3) potassium superstructure was observed by LEED. TOF-SARS experiments ruled out the adsorption of potassium in the on-top, bridge and four-fold hollow site. The only site which is in agreement with all experimental results is the substitutional site where K replaces an Fe atom of the topmost layer of the crystal. This is the first time a substitutional adsorption site has been found on a bcc surface. On an fcc surface such an adsorption site has been found recently for adsorption of sodium and potassium on Al(111).     

铅盐PbS(001)表面几何结构特性

用第一性原理方法计算了铅盐PbS的体晶格常数和 （001） 表面的几何结构,计算结果表明铅盐 （001）表面几何结构具有弛豫和褶皱的特性,为铅盐的广泛应用提供了理论参考数据.     

随机系统的Peuteman-Aeyels指数稳定性定理

把Peuteman-Aeyels指数稳定性定理从确定性系统推广到随机系统.并借此讨论了随机混杂系统的均方指数镇定问题,得出了系统在同步切换下可镇定的充分必要条件.