面向对象程序设计与期权定价模型的数值求解

金融衍生品领域的高效数值模拟计算是当前的研究热点，描述金融衍生品定价的Black-Scholes方程，其参数的改进和数值求解对计算结果与实际结果的拟合，会产生大的影响。本文对Black-Scholes方程的参数改进和数值求解进行了一些研究和分析。 论文深入研究和分析了在金融计算领域的FNR的数值计算软件包。对它的特点，及其中的类成员、函数、总体设计和细节设计进行了详细的剖解。论文对Black-Scholes公式的σ的改进模型，随机波动率模型进行了理论描述和定量解释，并用数值结果给出了改进后的效果比较。在改进Black-Scholes模型的基础上，论文对随机波动率(SV)模型进行展开，从Monte-Carlo的模拟和有限差分的模拟两方面 对Black-Scholes模型的波动率进行了改进。在此基础上，利用Heston的随机波动模型基本理论，给出改进后Black-Scholes方程的数值解。基于面向对象的程序设计，论文同时给出了用神经计算方法数值求解非线性的Black-Scholes方程的算法和程序实现，并用中国权证市场的实际数据进行了测试，与解释解的结果进行了比对。数值结果表明，神经计算方法虽然在前期数据训练和运行速度方面较数值方法慢，但是却可以在精度上很好的逼近实际结果。因为人工神经网络方法可以在没有任何限制参数的建模假定下，由数据确定模型的结构和参数，对于金融市场这样一个存在丰富的高质量的数据，而可检验的模型却相对缺乏或不准精确的实践领域，正受到越来越多的重视。 在本文中用有限差分方法解决Heston随机波动率模型求解了欧式期权定价问题，实际上有限差分方法是非常适用于美式期权定价，但是本文由于时间关系未能实现有限差分方法解决美式期权定价问题，但是对于美式期权定价问题我大致介绍了如何基于Heston的随机波动率模型求解的数学思路，做为对未来的研究的很好展望。同时在人工神经网络方法中，我设计了基于已实现的模型的另一种专家模型。因为新型的专家模型对价格做了更详细的分类，在数据训练之后，会得到比已实现的模型更好的结果。

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Entropy of Kaluza-Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza-Klein black hole in Einstein-Maxwell-Dilaton theory. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza-Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza-Klein black hole is reproduced by Cardy formula. (C) 2010 Elsevier B.V. All rights reserved.

Studies on the electrical conductivity of carbon black filled polymers

The conductivity mechanism for a carbon black (CB) filled high-density polyethylene (HDPE) compound was investigated in this work. From the experimental results obtained, it can be seen that the relation between electrical current density (J) and applied voltage across the sample (V) coincides with Simmons's equation (i.e., the electrical resistivity of the compound decreases with the applied voltage, especially at the critical voltage). The minimum electrical resistivity occurs near the glass transition temperature (T-g) of HDPE (198 K). It can be concluded that electron tunneling is an important mechanism and a dominant transport process in the HDPE/CB composite. A new model of carbon black dispersion in the matrix was established, and the resistivity was calculated by using percolation and quantum mechanical theories. (C) 1996 John Wiley & Sons, Inc.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

A lattice Boltzmann equation for waves

We propose a lattice Boltzmann model for the wave equation. Using a lattice Boltzmann equation and the Chapman-Enskog expansion, we get 1D and 2D wave equations with truncation error of order two. The numerical tests show the method can be used to simulate the wave motions.

Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.