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July 15,2011
Volume 4,Issue 13
Pages -
Subject Area:Applied Mathematics,Elliptic Partial Differential Equations

Title: Simple criteria for nonsingular block H-matrix

Authors: TANG Min, ZHANG Juan
PP: 1243-1247
Abstract: Nonsingular (block) H-matrix is an important class of special matrix with extensive applications. The paper applies block matrix technology and the properties of matrix norm, constructs positively diagonal matrix, and gives some new criteria for nonsingular block H-matrix on the basis of dot H-matrix. Then it extends these methods to the conditions of block irreducible matrix and block non-zero element chain matrix. Finally, it illustrates the effectiveness with a numerical example.
Keywords: applied mathematics; nonsingular block H-matrix; positive diagonal matrix; irreducible matrix; non-zero element chain

Title: Property of g-expectation with comonotonic subadditivity for some backward stochastic differential equations

Authors: XU Yuzhen
PP: 1238-1242
Abstract: In this paper, under the basic assumption of the generator, through the definition of g-expectation and conditional g-expectation in Lp(1 Keywords: stochastic analysis; g-expectation; Lp space; comonotonic subadditivity

Title: Computation of VaR and its optimization based on historical simulation method

Authors: CHEN Yufeng, SUN Hongxiang, WEN Qiaoyan
PP: 1231-1237
Abstract: The paper analyzes the computation of value at risk (VaR) by historical simulation method, and improves the precision of VaR by increasing weights and fluctuation ratio. It also discusses the improvement of VaR estimation by extreme value theory, which makes VaR obtained by using historical data give the shape of the whole tail.
Keywords: applied mathematics; value at risk; historical simulation method; extreme value theory

Title: The optimal investment-consumption strategy with stochastic market

Authors: MA Cunyi, YAN Dingqi
PP: 1225-1230
Abstract: In this paper, a multi-period investment-consumption problem that involves utility from both current and previous consumption is investigated. The random return of risky asset depends on the state of the market during any period where the market process is assumed to follow a Markov chain. An explicit expression is obtained for the optimal investment and consumption strategies by dynamic programming.
Keywords: applied mathematics; Markov chain; investment-consumption; utility; dynamic programming

Title: Short-term traffic flow prediction based on the rolling forecast and residual correction

Authors: TANG Xiangjin, LU Junhua
PP: 1219-1224
Abstract: Real-time and accurate traffic flow prediction is the premise and key of traffic control and induction. Because of the raw traffic data scarce, based on grey system characteristic of small samples, the rolling forecast is used to make residual inspection for reliable traffic flow prediction. In consideration of the metabolism of data, the computation can be reduced. At the same time, the analysis is made for the change rule of rolling residual, the grey forecasting model based on the monotonous interval is established and the original prediction data is compensated through residual correction in order to make prediction fit the original data better. Finally, the example computation and the model accuracy test show that this method has a high precision.
Keywords: applied mathematics and statistics; traffic flow prediction; grey system theory; rolling forecast; residual correction

Title: A solution of backward stochastic differential equations and Choquet-expectation

Authors: DENG Xiaohong, GAO Wei, YANG Zhi
PP: 1213-1218
Abstract: This paper introduces a class of solution to backward stochastic differential equations (BSDE) with coefficient g which is Lipschitz continuous in y and uniformly continuous in z. Recalls some properties of the solution and Choquet expectation, names the solution as g*-expectation. When d=1 and g is a continuous function, gets an equal proposition which g*-expectation can be expressed as a Choquet expectation.
Keywords: financial mathematics; g*-expectation; Choquet-expectation; comonotonic additive

Title: Explicit-implicit and implicit-explicit algorithm for solving the payment of dividend Black-Scholes equation

Authors: WU Lifei, YANG Xiaozhong
PP: 1207-1212
Abstract: This paper constructs the explicit-implicit and implicit-explicit schemes for solving the payment of dividend Black-Scholes equation. It gives the convergence, stability and error estimates of schemes. The analysis demonstrates that the schemes are second order and have the same amount of calculation, which is less than the Crank-Nicolson scheme’s. Finally, the numerical examples show the feasibility and effectiveness of the schemes.
Keywords: financial mathematics; option pricing; explicit-implicit scheme; implicit-explicit scheme; stability; the payment of dividend Black-Scholes equation

Title: Characteristic function of Ornstein-Uhlenbeck process

Authors: CHEN Duhua, XIE Yuquan
PP: 1203-1206
Abstract: In order to make full use of Ornstein-Uhlenbeck process(O-U process) in engineering, finance and so on, the characteristic function which is one important kind of the numerical characteristics of O-U process is mainly researched in this paper. According to the features of O-U process, firstly the characteristic function of the normal part of one-parameter and two-parameter O-U process is obtained by the way of calculating mean and variance in this paper, then the characteristic function of whole O-U process is computed based on the definition of characteristic function ψX(λ)=Eexp{i λX}on the condition of x0 is constant and x0 obeys normal distribution. Finally it is generalized to the case of multi-parameter one-dimensional similarly.
Keywords: probability and mathematical statistics; Ornstein-Uhlenbeck process; one-parameter; multi-parameter; one-dimensional; characteristic function

Title: Truncation regularization method for Cauchy problem for the Laplace equation in rectangle domain

Authors: LI Wenqi, FU Chuli
PP: 1193-1202
Abstract: This paper considers a Cauchy problem for the Laplace equation with nonhomogeneous Neumann data in a rectangle domain {(x, y)|0 Keywords: partial differential equations; ill-posed problem; truncation regularization method; Cauchy problem for the Laplace equation; Neumann data; regularization parameter

Title: A model combining weighted total variation and wavelet for image-inpainting

Authors: WANG Yan, GUO Dinghui
PP: 1189-1192
Abstract: This paper studies a partial differential equation model which combines weighted total variation approach and wavelet approach to solve the image inpainting problem. This method combines advantages of total variation and wavelet transform. Moreover, using the method of weighted total variation makes it more adaptive. The experiment shows that the effect of inpainting is better which preserves the texture and reduces the Gibbs phenomenon.
Keywords: partial differential equations; weighted total variation; wavelet; image inpainting

Title: An improved algorithm for computing differential characteristic set

Authors: Temuer CHAOLU, HAN Xiaoyan, TIAN Yi
PP: 1182-1188
Abstract: A pure algebra form characteristic set algorithm of polynomial system is generalized to differential case and a simplified mechanical algorithm for determining differential characteristic set of differential polynomial system is proposed. The algorithm can overcome, at some extend, the heavy work load difficulty in computing differential characteristic set and can be applied to wide range of related fields of differential equations, such as symmetry, conservation law computations.
Keywords: mathematical mechanization; Wu’s method; differential polynomial system; differential characteristic set; algorithm

Title: Uniqueness of meromorphic functions

Authors: LI Xianjun, CHEN Liucai
PP: 1174-1181
Abstract: The uniqueness of meromorphic functions concerning common value or common small function is an important part of the uniqueness theory of the meromorphic functions. This paper studies the problem of Hayman from the view of weighted sharing small function, namely, investigated uniqueness theory about nonconstant meromorphic functions f, whose multiplicity of zero and pole are not less than n, weighted sharing one small function with one of their derivatives. It also studies the particular condition there f are entire functions. The theories have improved the existed results.
Keywords: fundamental mathematics; meromorphic function; share small function; uniqueness

Title: Theory and algorithm for optimal solution set of linear programming

Authors: PENG Yuelin
PP: 1163-1173
Abstract: Four properties, a necessary-sufficient condition and an algorithm for the optimal solution set of linear programming have been established. An in-depth discussion about time complexity was developed and then it was concluded that the algorithm is polynomial.
Keywords: operations research; linear programming; optimal solution set; necessary and sufficient condition; time complexity; polynomial time algorithm

Title: Sample average approximation method for solving a class of stochastic mixed complementarity problems

Authors: HE Zhifeng, LIN Guihua
PP: 1155-1162
Abstract: In this paper, a class of stochastic mixed complementarity problems (SMCP) is considered. The Fischer-Burmeister function is used to reformulate the SMCP as nonsmooth equations. Then, the sampling average approximation techniques based on Monte Carlo method are employed to propose a semismooth Newton method for solving the equations. Convergence analysis is given as well. The results are finally applied to traffic equilibrium problems and some preliminary numerical results are reported.
Keywords: nonlinear programming; stochastic mixed complementarity problem; sample average approximation; semismooth Newton method; Monte Carlo method; traffic equilibrium problem

Title: Wavelet characterization for multipliers on Hardy space and BMO space

Authors: YANG Qixiang
PP: 1149-1154
Abstract: In this paper, wavelet characterization of multiplier spaces for the end point space cases has been considered. Multiplier spaces have been studied heavily since 1950s and stay always as an active topic. Before, one used the capacity of compact set on Sobolev spaces to characterize multiplier spaces and to study the applications related to multiplier spaces. Part of multiplier spaces has no unconditional basis. Here wavelet methods and atomic decomposition are introduced, and the structure of multiplier spaces is analyzed through the following conceptions: some special decomposition of function product, known wavelet characterization of certain function spaces, dual property etc. The multiplier spaces on fractional Hardy spaces has only element 0 and the multiplier spaces on fractional BMO is the intersection of two special spaces.
Keywords: fundamental mathematics real analysis; multiplier spaces; Daubechies wavelet; decomposition of function product; fractional Hardy space; fractional BMO spaces

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