GARCH模型中美式亚式期权价值的蒙特卡罗模拟算法

我们运用 Longstaff和 Schwartz最近提出的用蒙特卡罗模拟法计算美式期权的方法在 GARCH模型中求解美式亚式期权 ,我们的结果表明和其它数值方法相比 ,这个方法不仅有相当的精确度 ,而且使用简便并具有更广泛的适用性 ,对于 GARCH模型中运用格点法难以求解的浮动执行价格的美式亚式期权同样可以得到稳定解 .     

基于扭曲混合Copula和ARMA-GARCH-t模型的投资组合风险分析——以上证综指、中证综合债和上证基金为例

利用扭曲混合Copula和ARMA-GARCH-t模型,对包含2015年股灾和2016年熔断期间的上证综指、中证综合债和上证基金的投资组合风险相关性进行建模分析。研究表明:扭曲混合Copula模型较混合Copula模型能更好地拟合各资产日收益率间的相关结构,尤其是"厚尾"特性。并运用蒙特卡罗模拟法计算各资产的风险价值、预期损失和中位数损失并讨论其差异性,以期为关注风险管理的人们提供更多借鉴。     

基于数值流形法的降雨入渗与坡面径流耦合算法研究

降雨时坡地的入渗-产流分析，是降雨型滑坡、泥石流等地质灾害机理研究中的重要课题之一.为实现边坡降雨-入渗-产流的全过程数值模拟，进一步提高计算效率，考虑将降雨入渗面视作坡面径流与坡体渗流的内部域，基于一维运动波方程和二维压力水头格式的Richards方程建立耦合模型，并推导出其总体控制方程，采用数值流形法(numerical manifold method, NMM)实现其数值求解，通过编制相应的计算程序分析了边坡降雨产流过程.数值分析结果表明：所建模型的计算结果与试验数据及前人模拟结果吻合良好，验证了该文模型及计算方法的有效性与可靠性；降雨强度越大，产流时间越早，坡面积水深度越大，对坡体内的水分分布影响范围越广.研究表明，所建模型能真实反映边坡降雨-入渗-产流全过程，可为降雨诱发的各类地质灾害分析提供计算依据.     

攀登伪蒙特卡罗积分法在Sobolev和Korobov空间中的随机化误差

攀登伪蒙特卡罗积分法是由伪蒙特卡罗与蒙特卡罗方法混合而成的一种新方法，它体现了两者的优点．本文研究这种积分法在Sobolev空间和Korobov空间中的随机化误差．我们证明攀登(λ，t，m，s)-网积分法在这两个空间中的随机化误差的渐近阶为n^3/2[logn]^(s-1)/2。     

非仿射随机波动率的欧式障碍期权定价

研究非仿射随机波动率模型的欧式障碍期权定价问题时,首先介绍了非仿射随机波动率模型,其次利用投资组合和It^o引理,得到了该模型下扩展的Black-Schole偏微分方程.由于这个方程没有显示解,因此采用对偶蒙特卡罗模拟法计算欧式障碍期权的价格.最后,通过数值实例验证了算法的可行性和准确性.     

二项线性随机效应模型的拟蒙特卡罗估计

讨论了如何运用拟蒙特卡罗方法对二项线性随机效应模型进行参数估计.首先写出观测数据的边缘对数似然函数,然后用拟蒙特卡罗方法将函数中的积分写成求和的形式,接着利用Newton-Raphson算法计算参数的极大似然估计.以一组种子数据为例,说明该方法是简单可行的.     

基于Copula的VsR度量与事后检验

估计VaR的传统方法有三种:协方差矩阵法、历史模拟法和蒙特仁洛模拟法。通常,文献中认为刚蒙特卡洛模拟法度量VaR有很多方面的优点。但是,本文通过实证检验发现,使用传统蒙特卡洛模拟法估计的VaR偏小,事后检验效果很不理想。本文引入Copula函数来改进传统的蒙特卡洛模拟法。Copula函数能将单个边际分布和多元联合分布联系起来,能处理非正态的边际分布,并且它度量的相关性不再局限于线性相关性。实证检验表明,基于Copula的蒙特卡罗模拟法可以更加准确地度量资产组合的VaR。     

波动性变化下的VaR历史模拟法实证研究

VaR(在险价值)方法是当今运用得最为广泛的金融市场风险度量方法。历史模拟法作为计算VaR的主要方法之一,其计算出来的VaR的风险度量效果需要得到现实金融市场数据的检验。本文通过选取上证综指日收益率的历史数据,分别在市场波动性不发生改变、市场波动性变大和市场波动性变小三种情况下对历史模拟法的有效性进行检验,检验结果表明在市场波动性不发生变化的情况下,历史模拟法计算的VaR能够有效地度量市场风险;在市场波动性变大的情况下,该方法会低估市场风险;在市场波动性变小的情况下,该方法会高估市场风险。通过对历史模拟法的计算原理进行分析,历史样本自身的时滞性是导致该方法在市场波动性发生变化时无效的原因。     

Duane-LR模型下复杂系统的动态可靠性增长评定

基于复杂系统可靠性增长试验的特点，运用Duane可靠性增长模型结合数理统计中的线性回归方法对新批次产品的可靠性参数进行预测。结合产品的少量现场试验数据，利用Bayes方法对系统的可靠性增长试验结果进行评定。文中首先给出了可靠性增长分析的模型，然后运用历次阶段试验中的可靠性增长数据建立动态参数的递推估计模型，在此基础上，运用随机变量函数的分布，给出各阶段可靠性增长试验中可靠性参数的Bayes估计。文中对Weibull、指数和二项分布三种试验结果进行分析，给出计算公式。     

蒙特卡罗方法计算定积分的进一步讨论

介绍了蒙特卡罗方法计算定积分的原理和方法.给出了用蒙特卡罗方法计算定积分的一个简单证明,从而揭示了蒙特卡罗方法和定积分定义间的内在联系.针对蒙特卡罗方法收敛慢的特点,提出将蒙特卡罗方法与相应的数值计算方法相结合,提高计算结果的精度.此外,将蒙特卡罗方法推广到反常积分上去.     

培养学生科学思维和创新能力的研究与实践——谈大学数学研究型教学

通过从一个导数值等式的证明谈起,探讨教师在课堂教学中如何根据教学内容创设能激起学生新异感的问题情景,启发和引导学生发散思考,类比、联想、猜想,探索和发现新问题并给出解答.使学生思维不断攀升,丰富教学内容,激发学生兴趣,培养学生科学思维方法和创新能力.     

Using the Tower of Hanoi puzzle to infuse your mathematics classroom with computer science concepts

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi puzzle. These concepts include, but are not limited to, conditionals, iteration, and recursion. Lessons, such as the one proposed in this article, are easily implementable in mathematics classrooms and extracurricular programmes as they are good candidates for ‘drop in’ lessons that do not need to fit into any particular place in the typical curriculum sequence. As an example for readers, the author describes how she used the puzzle in her own Number Sense and Logic course during the federally funded Upward Bound Math/Science summer programme for college-intending low-income high school students. The article explains each computer science term with real-life and mathematical examples, applies each term to the Tower of Hanoi puzzle solution, and describes how students connected the terms to their own solutions of the puzzle. It is timely and important to expose mathematics students to computer science concepts. Given the rate at which technology is currently advancing, and our increased dependence on technology in our daily lives, it has become more important than ever for children to be exposed to computer science. Yet, despite the importance of exposing today's children to computer science, many children are not given adequate opportunity to learn computer science in schools. In the United States, for example, most students finish high school without ever taking a computing course. Mathematics lessons, such as the one described in this article, can help to make computer science more accessible to students who may have otherwise had little opportunity to be introduced to these increasingly important concepts.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

A multivariate adaptive regression splines cutting plane approach for solving a two-stage stochastic programming fleet assignment model

The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated.     

摸彩决策的数学模型

生活中 ,摸彩的人们总以为越先摸 ,中彩的可能性越大 ,其实不然 !为此本文从概率角度建立了数学模型 ,证明了每个摸彩者中彩的机会均等 ,与先后摸彩顺序无关 .同时 ,通过分析在中彩时 ,已摸过的彩票数目的数学期望 ,向彩票发行者提出了几点建议 .     

Vanishing pressure limits of Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas

The Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas with a small parameter are considered. Unlike the polytropic or barotropic gas cases, we find that firstly, as the parameter decreases to a certain critical number, the two-shock solution converges to a delta shock wave solution of the same system. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the solution is nothing but the delta shock wave solution to the zero-pressure relativistic Euler system. Meanwhile, the two-rarefaction wave solution tends to the vacuum solution to the zero-pressure relativistic system, and the solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution to the zero-pressure relativistic system as pressure vanishes.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

考虑充电设施重入的电动汽车旅行商问题研究

出于减少环境危害和响应相关法规的考虑,物流企业开始逐步将运输车辆转变为电动汽车;而由于电动汽车的续航里程有限,对电动汽车的路径优化也将涉及充电设施。充电设施的“重入”是指电动汽车返回之前已经通过的充电设施进行充能的现象,它的存在需要改变经典旅行商问题模型中的“子回路约束”。本文聚焦于充电设施的“重入”,构建了一个无需预估充电设施重入次数上限的电动汽车旅行商问题模型,并通过引入路径可行性判别方法和增加充电设施选择与重复策略,设计了一种改进蚁群算法对问题进行求解。结果表明:与未考虑重入的模型相比,本文提出的考虑充电设施重入的模型能在电动汽车电池容量较低的情况下求出最优解,同时也能够使充电设施承担多次充电任务,从而在较少充电设施情况下依然能够得到可行的最优路径。     

基于主客观信息综合判断的非线性拉开档次法

针对以最大程度的拉开被评价对象间差异的综合评价问题,通过分析线性拉开档次法存在的局限性,本文提出了一种基于主客观信息综合判断的非线性拉开档次法,旨在进一步丰富和完善拉开档次法的理论知识。首先对线性拉开档次法进行简单的介绍,并分析了线性拉开档次法的局限性;然后提出前提假设,给出非线性因子选取的原则以及确定指标序关系的方法,并给出排序后相邻指标重要程度比值的选取方法,根据评价原则利用规划模型求解各评价指标的权重系数,利用求得的指标权重采用非线性集结模型计算最终的评价结果;最后用一个算例验证了方法的有效性。     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.