随机利率Vasicek模型下的欧式缺口期权的定价研究

研究随机利率Vasicek模型下欧式缺口期权的定价问题,利用偏微分方程方法给出了欧式缺口看涨期权和看跌期权的定价公式,并且是Vasicek利率模型下标准欧式期权定价公式的一种推广.     

分形布朗运动下有交易成本的外汇期权定价

研究了有交易成本的分形Black-Scholes外汇期权定价问题.基于汇率的分形布朗运动分布假设,运用分形布朗运动的性质和随机微积分方法,得到了欧式外汇期权价格所满足的偏微分方程.最后,建立离散时间条件下的非线性期权定价模型,并且通过解期权价格的偏微分方程给出了有交易成本的欧式外汇期权定价公式.     

基于随机波动率状态转移特征的上证50ETF期权定价

期权定价模型的构建过程中，单因子随机波动率模型生成的波动率曲线形状与波动率水平相关性微弱，且无法确切反映波动过程的状态转移特征。为此，本文使用连续马尔可夫链刻画波动状态，在Heston模型的基础上，针对其方差动态过程中所有参数均为波动状态任意函数的情景，得到了一类具有状态转移特征的随机波动率模型；进一步，根据条件仿射模型的特征函数，结合波动路径的蒙特卡罗模拟，实现了欧式期权半解析定价，其中，采用基于粒子滤波的极大似然估计方法估计模型参数；特别地，对上证50ETF期权进行了实证研究。结果表明：具有状态转移特征且方差的基准长期均值及波动率均依赖于波动状态的随机波动率模型，能够显著提升上证50ETF期权定价的准确性和稳健性。     

随机利率下奇异期权的定价公式

在随机利率条件下,借助于测度变换获得了复合看涨期权的一般的定价公式,同时利用鞅理论和Girsanov定理,在利率服从于扩展的Vasicek利率模型时,得到了复合看涨期权精确的定价公式.用同样的方法,考虑了预设日期的重置看涨期权的定价问题,在利率服从同样的利率模型时,获得了重置看涨期权的定价公式.数值化的结果进一步说明了当利率遵循扩展的Vasicek利率模型时,B-S看涨期权的价格关于标的资产的价格是严格单调递增的,复合看涨期权的Geske公式是可以推广到随机利率的情况.     

投资项目的期权评价与最优投资规则

本文介绍了不确定环境下的投资项目的期权评价方法和最优投资规则，研究了单期项目和连续投资项目的投资决策问题，探讨了实物期权评价方法与传统的净现值评价方法中最优投资规则的差异，并对影响最优投资规则的差异因素进行了敏感性分析，得出了直观而有实用价值的结论。     

基于随机波动率模型的上证50ETF期权定价研究

传统上,期权定价主要基于Black-Scholes (B-S)模型。但B-S模型不能描述时变波动率以及解释"波动率微笑"现象,导致期权定价存在较大的误差。随机波动率模型克服了B-S模型的这些缺陷,能够合理地刻画波动率动态性和波动率微笑。基于此,本文考虑随机波动率模型下的期权定价问题,并针对我国上证50ETF期权进行实证分析。为了解决定价模型的参数估计问题,采用上证50ETF及其期权价格数据,建立两步法对定价模型的参数进行估计。该估计方法保证了定价模型在客观与风险中性测度下的一致性。采用2016年1月到2017年10月的上证50ETF期权价格数据为研究样本,对随机波动率模型进行了实证检验。结果表明,无论是在样本内还是样本外,随机波动率模型相比传统的常数波动率B-S模型都能够获得明显更为精确和稳定的定价结果,B-S模型的定价误差总体偏大且呈现较高波动,凸显了随机波动率对于期权定价的重要性。另外,随机波动率模型对于短期实值期权的定价相比对于其它期权的定价要更精确。     

随机波动模型下算术亚式期权的Monte Carlo模拟定价

在随机波动模型下,研究亚式期权的定价问题.推导出了标的资产及其随机波动模型的路径,利用对偶变量法对亚式期权进行数值模拟计算,并对随机波动模型下与B-S模型下的欧式期权和亚式期权定价结果进行比较,最后给出了具有固定敲定价格和浮动敲定价格的算术亚式期权的数值计算结果.     

美式期权定价问题的数值方法

本文研究美式股票看跌期权定价问题的数值方法。通过将问题转化为等价的变分不等式方程，分别建立了半离散和全离散有限元逼近格式。并给出了有限元解的收敛性和稳定性分析。数值实验表明本文算法是一个高效和收敛的算法。     

随机利率下服从分数O-U过程的二元期权定价

本文考虑在扩展的Vasicek模型和分数O-U过程驱动下的二元期权定价问题。运用拟鞅方法,得到了在随机利率情形下,股票价格在分数O-U过程驱动下的二元期权的定价公式。     

考虑信用风险的亚式期权定价

在结构化模型下,考虑标的资产的红利收益及企业债务为确定和随机两种情况,采用鞅方法得到有信用风险的连续几何平均亚式看涨和看跌期权的定价公式。且公式具有Black-Scholes平价关系。     

一种改进的随机次梯度方法的快速收敛性

1引言考虑如下优化问题: min f(x)=sum from i=1 to m f_i(x),s.t. x∈X (1)其中,f_i∶R~n→R是凸函数且f_i不可微,X是R~n上的非空闭凸子集．解(1)的主要方法     

Stochastic Nonlinear Complementarity Problems: Stochastic Programming Reformulation and Penalty-Based Approximation Method

We consider a class of stochastic nonlinear complementarity problems. We first reformulate the stochastic complementarity problem as a stochastic programming model. Based on the reformulation, we then propose a penalty-based sample average approximation method and prove its convergence. Finally, we report on some numerical test results to show the efficiency of our method.     

Stochastic asymptotical stability for stochastic impulsive differential equations and it is application to chaos synchronization

In this paper, the stochastic asymptotical stability of stochastic impulsive differential equations is studied, and a comparison theory about the stochastic asymptotical stability of trivial solution is established. From the comparison theory, we can find out whether the stochastic impulsive differential system is stochastic asymptotically stable by studying the stability of a deterministic comparison system. As an application of this theory, we study the problem of chaos synchronization in Chua circuit using impulsive method. Finally, numerical simulation is employed to verify the feasibility of our method.     

Application of rational expansion method for stochastic differential equations

By means of the Hermite transformation, a new general ansätz and the symbolic computation system Maple, we apply the Riccati equation rational expansion method [24] to uniformly construct a series of stochastic non-traveling wave solutions for stochastic differential equations. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions. The method can also be applied to solve other nonlinear stochastic differential equation or equations.     

广义随机KP方程的椭圆周期解

利用Hermite变换和Jacobi椭圆函数展开法研究(2+1)-维广义随机Kadomtsev-Petviashvili方程,并给出了它的随机椭圆周期解及随机孤立波解.     

Stochastic Galerkin techniques for random ordinary differential equations

Over the last decade the stochastic Galerkin method has become an established method to solve differential equations involving uncertain parameters. It is based on the generalized Wiener expansion of square integrable random variables. Although there exist very sophisticated variants of the stochastic Galerkin method (wavelet basis, multi-element approach) convergence for random ordinary differential equations has rarely been considered analytically. In this work we develop an asymptotic upper boundary for the L ₂-error of the stochastic Galerkin method. Furthermore, we prove convergence of a local application of the stochastic Galerkin method and confirm convergence of the multi-element approach within this context.     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise

The paper is devoted to the study of stochastic heat equations driven by Lévy noise. Applying the WKB method, we obtain multiplicative small time and semiclassical asymptotics for the Green functions and for solutions of the Cauchy problem for the heat equation under some natural additional assumptions on their coefficients. The first step in this construction consists in solving the corresponding stochastic Hamilton-Jacobi equations which constitute the "classical part" of the semiclassical approximation. In its turn, the corresponding Hamilton-Jacobi equations can be solved via solutions of the corresponding Hamiltonian systems, which gives rise to the method of stochastic characteristics. The relevant theory of stochastic Hamiltonian systems and stochastic Hamilton-Jacobi equations was developed in our previous papers. Here we put the final rung on the ladder: stochastic Hamiltonian systems, stochastic Hamilton-Jacobi equations, stochastic heat equations.     

Numerical comparison of three stochastic methods for nonlinear PN junction problems

We apply the Monte Carlo, stochastic Galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces. Instead of dividing the rough surface into slices, we use stochastic mapping to transform the original deterministic equations in a random domain into stochastic equations in the corresponding deterministic domain. A finite element discretization with the help of AFEPack is applied to the physical space, and the equations obtained are solved by the approximate Newton iterative method. Comparison of the three stochastic methods through numerical experiment on different PN junctions are given. The numerical results show that, for such a complicated nonlinear problem, the stochastic Galerkin method has no obvious advantages on efficiency except accuracy over the other two methods, and the stochastic collocation method combines the accuracy of the stochastic Galerkin method and the easy implementation of the Monte Carlo method.     

基于列随机矩阵的逐次差分代换与正半定型的机械化判定

本文选择列随机平均矩阵T_n作为基本代换矩阵,建立了基于T_n的逐次差分代换方法.获得了R_+~n上正半定型,不定型判定的充要条件.并进一步证明了:正定型的差分代换集序列正向终止.根据这些结果编写的Maple程序TSDS3,能够自动证明代数型不等式,对不成立的不等式总能输出反例.该程序虽可能不停机,但大量的应用实例证实了该方法的实用性.