存贷利率不等下具有随机跳跃收入的消费与投资策略

研究贷款利率大于存款利率下具有随机跳跃收入的最优策略,拓展了Merton模型.给出了财富预算方程,运用动态规划原理及随机分析导出该问题的HJB方程,并由此得到一般情形下抽象形式的解.在一类特殊HARA情形下讨论了具有显式反馈形式的最优消费和投资策略.     

存贷利率不等下具有随机跳跃收入的消费与投资策略

研究贷款利率大于存款利率下具有随机跳路收入的最优策略,拓展了Ｍｅｒｔｏｎ模型。给出了财富预算方程,运用动态规划原理及随机分析导出该问题的ＨＪＢ方程,并由此得到一般情形下抽象形式的解。在一类特殊ＨＡＲＡ情形下讨论了具有显式反馈形式的最优消费和投资策略。     

带有随机跳跃干扰的线性二次随机最优控制问题

给出一类布朗运动和泊松过程混合驱动的正倒向随机微分方程解的存在唯一性结果, 应用这一结果研究带有随机跳跃干扰的线性二次随机最优控制问题,并得到最优控制的显式形 式,可以证明最优控制是唯一的.然后,引入和研究一类推广的黎卡提方程系统,讨论该方程系统 的可解性并由该方程的解得到带有随机跳跃干扰的线性二次随机最优控制问题最优的线性反馈.     

部分信息下极大终止时期望对数效用及价值测算

研究部分信忠下极大化终止时刻期望对数效用的最优投资策略问题．代替随机动态规划方法，利用Ito公式及非线性滤波技术，直接导出了部分信息下最优投资策略的显式解，并给出了简洁的信息价值测算公式．     

具有异常波动市场的消费与投资策略

讨论了异常波动市场中容许借贷的消费与投资策略问题,阐述了随机最优控制理论应用于现代金融理论研究中的一种方法.首先给出了金融市场中不确定性的随机模型,利用It^o公式,得到了与消费及投资策略有关的财富过程的随机微分方程,并建立了最优消费与投资问题的随机控制模型.根据随机最优控制理论,导出了目标函数满足的Hamilton-Jacobi-Bellman(HJB)方程.通过对HJB方程的讨论,得到了最优消费与投资策略的分段表示函数,并就Hara效用函数进行讨论,得到了具体的消费与投资策略.     

带Poisson跳的线性二次随机微分博弈及其在鲁棒控制中的应用

研究了一类带Poisson跳扩散过程的线性二次随机微分博弈,包括非零和博弈的Nash均衡策略与零和博弈的鞍点均衡策略问题．利用微分博弈的最大值原理,得到Nash均衡策略的存在条件等价于两个交叉耦合的矩阵Riccati方程存在解,鞍点均衡策略的存在条件等价于一个矩阵Riccati方程存在解的结论,并给出了均衡策略的显式表达及最优性能泛函值．最后,将所得结果应用于现代鲁棒控制中的随机H₂/H_∞控制与随机H_∞控制问题,得到了鲁棒控制策略的存在条件及显式表达,并验证所得结果在金融市场投资组合优化问题中的应用．     

正倒向随机微分方程与一类线性二次随机最优控制问题

讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制 问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果 研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到 由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其 对应的Riccati方程.     

一个风险敏感最优控制问题的随机最大值原理及在投资选择中的应用

在本文, 我们主要研究了一类产生于金融市场中投资选择问题的风险敏感最优控制问题. 用经典的凸变分技术, 我们得到了该类问题的最大值原理. 最大值原理的形式相似于风险中性的情形. 但是, 对偶方程和变分不等式明显地依赖于风险敏感参数 γ. 这是与风险中性情形的主要区别之一. 我们用该结果解决一类最优投资选择问题. 在投资者仅投资国内债券和股票的情况下, 前人用贝尔曼动态规划原理所得的最优投资策略仅是我们结果的特殊形式. 我们也给了一些数值算例和图, 他们显式地解释了最大期望效用和模型中参数的关系.     

一类带随机跳跃的完全耦合的线性二次随机控制问题

研究一类带随机跳跃的完全耦合的线性二次随机控制问题. 得到了最优控制的显式解, 并可以证明最优控制是唯一的. 引入了一类推广的黎卡提方程并讨论了其可解性. 利用这一类推广的黎卡提方程的解, 得到了上述带随机跳跃的最优控制问题的线性状态反馈调节器.     

跳跃扩散股价的最优投资组合选择

假定股票价格服从跳跃扩散过程.在传统均值-方差组合投资模型基础上,最大化最终收益的期望及最小化最终财富的方差.引进一个随机线性二次最优控制问题作为原问题的近似问题.证明了一个状态为跳跃扩散过程的一般最优控制问题的验证性定理.应用验证性定理求解HJB(Hamilton-Jacobi-Bellman)方程得到了原问题的最优策略.最后还给出了原问题有效前沿的表达式.     

非线性演化方程的新Jacobi椭圆函数解

基于sinh-Gordon方程的椭圆函数解,构造新的试探解来扩展sinh-Gordon方程展开法.利用该方法研究了KdV-mKdV方程,双sine-Gordon方程和BBM方程,获得了这些方程的新Jacobi椭圆函数解.该方法也能用来求解其他数学物理中的非线性演化方程.     

Zakai equation of nonlinear filtering with unbounded coefficients. The case of dependent noises

In this paper, we prove that the unnormalized filter associated with nonlinear filtering problems with dependent noises and a one-dimensional observations process the coefficients of which are unbounded solves a parabolic stochastic partial differential equation, the Zakai equation. The robust form of the Zakai equation is also computed.     

Numerical solution of GRLW equation using Sinc-collocation method

In this paper, we present a meshfree technique for the numerical solution of the generalized regularized long wave (GRLW) equation. This approach is based on a global collocation method using Sinc basis functions. The propagation of single solitons and the interaction of two solitary waves are used to validate the method which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the method.     

A Class of Sparse Spectral Operators for Inversion of Powers of the Laplacian in N Dimensions

For inversion of the Laplacian subject to Dirichlet boundary conditions and, more generally, for the kth power of the Laplacian subject to boundary conditions on the function and its first k – 1 derivatives in the normal coordinate, there is a sparse symmetric, well-conditioned, projection of the operator that results from an expansion in associated Legendre polynomials.     

Matrix algorithms for solving (in)homogeneous bound state equations

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems.     

On the quantum master equation under feedback control

The nature of the quantum trajectories, described by stochastic master equations, may be jump-like or diffusive, depending upon different measurement processes. There are many different unravelings corresponding to different types of stochastic master equations for a given master equation. In this paper, we study the relationship between the quantum stochastic master equations and the quantum master equations in the Markovian case under feedback control. We show that the corresponding unraveling no longer exists when we further consider feedback control besides measurement. It is due to the fact that the information gained by the measurement plays an important role in the control process. The master equation governing the evolution of ensemble average cannot be restored simply by eliminating the noise term unlike the case without a control term. By establishing a fundamental limit on performance of the master equation with feedback control, we demonstrate the differences between the stochastic master equation and the master equation via theoretical proof and simulation, and show the superiority of the stochastic master equation for feedback control.     

求一类非线性偏微分方程解析解的简洁构造算法

通过引入一个变换,利用齐次平衡原理和选准一个待定函数来构造求解一类非线性偏微分方程解析解的算法.作为实例,我们将该算法应用到了mKdV方程,KdV-Burgers方程和KdV-Burgers-Kuramoto方程.借助符号计算软件Mathematica获得了这些方程的解析解.不难看出,该方法不仅简洁,而且有望进一步扩展.     

Soave汽液平衡模型在苯与乙烯烷基化反应动力学中的应用

实验在等温无梯度反应器内进行 ,使用 12 0～ 140mesh的FX - 0 2催化剂 ,用量 85 0～ 45 0 0mg,温度 130～2 10± 1℃ ,压力 1 95± 0 0 2MPa ,搅拌转速 10 0 0rpm下 ,研究了苯与乙烯烷基化反应动力学。在研究过程中 ,利用Soave汽液平衡模型计算了苯与乙烯烷基化反应中体系的汽液相平衡 ,从而通过计算 ,取得了动力学实验中不能直接测得的液相组成数据 ,并在此基础上进行了动力学模型的参数估值。参数估值过程采用改进的Gauss New ton法 ,以最小二乘为准则直接对常微分形式的反应动力学模型进行估值。对反应动力学模型的方差分析和残差分析的显著性检验表明 ,反应动力学模型基本无缺陷 ,其对实验数据的拟合也比较好。由此表明 ,Soave汽液平衡模型应用于苯与乙烯的烷基化反应动力学计算是成功的     

Perturbation of solutions of ordinary linear homogeneous differential equations of the second order

In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order.     

A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations

A three-step wavelet Galerkin method based on Taylor series expansion in time is proposed. The scheme is third-order accurate in time and O(2^?jp ) accurate in space. Unlike Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving non-linear problems. The compactly supported orthogonal wavelet bases D6 developed by Daubechies are used in the Galerkin scheme. The proposed scheme is tested with both parabolic and hyperbolic partial differential equations. The numerical results indicate the versatility and effectiveness of the proposed scheme.