Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options

We use the Malliavin integration by parts formula in order to provide a family of representations of the joint density (which does not involve Dirac measures) of (X_θ, X _{θ + δ}), where X is a d-dimensional Markov diffusion (d ≥ 1), θ > 0 and δ > 0. Following Bouchard et al. (2004), the different representations are determined by a pair of localizing functions. We discuss the problem of variance reduction within the family of separable localizing functions: We characterize a pair of exponential functions as the unique integrated-variance minimizer among this class of separable localizing functions. We test our method on the d-dimensional Brownian motion and provide an application to the problem of American options valuation by the quantization tree method introduced by Bally et al. (2002). MSC 1991 Subject Classifications: Primary 60H07 65C05, secondary 49-00     

Front-Tracking Finite Difference Methods for the Valuation of American Options

This paper is concerned with the numerical solution of the American option valuation problem formulated as a parabolic free boundary/initial value model. We introduce and analyze a front-tracking finite difference method and compare it with other commonly used techniques. The numerical experiments performed indicate that the front-tracking method considered is an efficient alternative for approximating simultaneously the option value and free boundary functions associated with the valuation problem.     

An efficient acceleration Monte Carlo simulation for pricing Asian option under variance gamma process by splitting

ABSTRACT

This paper proposes a hybrid acceleration method for pricing Asian options with arithmetic average under variance gamma process. We split the payoff of Asian option into two parts, the first part is a small probability event, so the importance sampling method is naturally used to reduce variance of simulation efficiently. The second part can be simplified as a semi-closed form, which also be considered as a conditional expectation formula, so it may reduce variance of simulations. Then the importance sampling method is also adapted to reduce variance of simulations further. To save computation cost for determining the optimal parameters in the importance sampling, a moment matching-based technique is proposed. Numerical results are given to show the high efficiency of our method. The idea used in this paper may also be applicable to price Asian option and Basket option under other time-changed Brownian motion and Heston models.     

基于拟蒙特卡罗方法的进化算法搜索鲁棒最优解的性能提高研究

鲁棒最优解在工程应用中具有十分重要的意义,它是进化计算的重要研究内容,也是研究难点．进化算法搜索鲁棒最优解时,通常使用蒙特卡罗积分(MCI)近似估计有效目标函数(EOF),但由于现有的原始蒙特卡罗方法(C-MC)近似精度不高,导致进化算法搜索鲁棒最优解的性能较差．文中提出用拟蒙特卡罗方法(Q-MC)估计有效目标函数,通过大量的数值实验,结果表明,与C-MC相比,文中所引入的Q-MC 方法、SQRT序列、SOBOL序列和Korobov点阵能更精确估计EOF,进而较大提高进化算法搜索鲁棒最优解的性能．     

基于蒙特卡洛方法的主动声纳信号检测性能分析

主动声纳信号检测性能的分析上,目前在计算机仿真中一般假定混响包络的统计特性符合瑞利分布模型。基于此模型,已经有了较完善的理论。然而,在现代高分辨声纳系统中,混响包络的统计特性并不符合瑞利分布模型。此时在接收机工作特性分析时存在大量繁琐的公式推导。因此该文采用蒙特卡洛（Monte Carlo）统计试验方法,实现对瑞利分布混响背景下的主动声纳信号检测性能分析。结合对接收机工作特性曲线的仿真,得出了检测概率的理论值和仿真结果的误差曲线。误差曲线表明,蒙特卡洛方法在主动声纳信号检测的性能评估中是可行的。     

面向服务软件中异常处理模块重要性的仿真分析方法

基于蒙特卡洛方法,提出异常处理模块重要性的影响因子,其中包括异常处理模块所对应的保护区的重要性以及异常处理模块自身的稳态故障率.基于贝叶斯理论,计算保护区的重要性;运用马尔可夫链的遍历性计算异常处理模块的稳态故障率.试图提出一种面向服务软件中异常处理模块重要性的定量分析方法,设计人员可以根据分析结果对重要度高的异常处理模块给予更多的关注.     

ReliaCloud‐NS: A scalable web‐based simulation platform for evaluating the reliability of cloud computing systems

This paper discusses the implementation, architecture, and use of a graphical web‐based application called ReliaCloud‐NS that allows users to (1) evaluate the reliability of a cloud computing system (CCS) and (2) design a CCS to a specified reliability level for both public and private clouds. The software was designed with a RESTful application programming interface for performing nonsequential Monte Carlo simulations to perform reliability evaluations of a CCS. Simulation results are stored and presented to the user in the form of interactive charts and graphs from within a web browser. The software contains multiple types of CCS components, simulations, and virtual machine allocation schemes. ReliaCloud‐NS also contains a novel feature that evaluates CCS reliability across a range of varying virtual machine allocations and establishes and graphs a CCS reliability curve. This paper discusses the software architecture, the interactive web‐based interface, and the different types of simulations available in ReliaCloud‐NS and presents an overview of the results generated from a simulation.     

磨矿粒度动态过程的一种快速Monte Carlo仿真方法

磨矿是降低矿物粒度的工业过程,产品粒度是磨矿过程的关键质量指标. 由于磨矿粒度难以在线检测且磨矿生产过程具有综合复杂特性,难以采用传统控制方法实现磨矿粒度的控制. 因此,建立磨矿粒度和关键工艺参数的动态模型对于磨矿运行控制和优化具有重要意义. 采用总量平衡原理获得磨矿粒度的微分方程模型多数情况下无法获得解析解. 而基于Monte Carlo （MC）方法的磨矿粒度模型能够精确模拟磨矿粒度分布的动态变化,但是其仿真效率低难以实用. 本文针对这一问题提出一种新的MC仿真方法： 在定总量方法的基础上引入新的颗粒移除机制,在移除过程中动态地分配各个粒级颗粒数目并保持破裂前后各个粒级颗粒所占总颗粒数的百分比不变,避免颗粒移除过程中由于粒级差异导致的抽样误差,且避免MC仿真速度随着仿真推进下降的问题. 仿真实验验证表明,本方法能够在保证一定精度前提下显著提高磨矿粒度MC仿真的计算速度. 最后,通过一个实例介绍了本文仿真模型在磨矿优化控制中的应用.     

Fast algorithms for computing the diameter of a finite planar set

Three algorithms for computing the diameter of a finite planar set are proposed. Although all three algorithms have (O(n ²) worst-case running time, an expected-complexity analysis shows that, under reasonable probabilistic assumptions, all three algorithms have linear expected running time. Experimental results indicate that two of these algorithms perform very well for some distributions, and are competitive with an existing method. Finally, we exhibit situations where these exact algorithms out-perform a published approximate algorithm.Research of the first author was supported by grant NSERC A 2422. Research of the second author was supported by grants NSERC A 9293, FCAC EQ-1678 and a Killam Senior Research Fellowship awarded by the Canada Council     

Forecast facilitated lot-for-lot ordering in the presence of autocorrelated demand

With consistent effort in setup reduction as encouraged by JIT principle, lot-for-lot ordering is gaining popularity in MRP applications. A lot-for-lot order is an immediate copy of the MPS (master production schedule) – direct reflection of demand forecasts. Since all levels of MRP plans are based on MPS, the accuracy of MRP is highly dependent of the accuracy of demand forecasting. In this paper, we are concerned about the impact of forecasting to the performance of a lot-for-lot MRP system when there is notable variability and autocorrelation in the underlying demand process (e.g., an AR(1) process). Specifically under a stationary AR(1) demand, we examine the performance of the MRP based on the most common EWMA forecast model, and then compare it with a minimum mean square error (MSE) forecast model. The notable findings of this study include: (1) MRP performance differs noticeably under the two different forecasting models. (2) The MSE-optimal forecasting performs no worse than the EWMA forecasting in all aspects of MRP applications.     

线性混杂系统优化控制的Monte Carlo统计预测方法

针对含扩散项的线性混杂切换系统优化控制问题, 为降低优化求解的计算复杂性, 提出了Monte Carlo统计预测方法. 首先通过数值求解技术把连续时间优化控制问题转化为离散时间的Markov决策过程问题; 然后在若干有限状态子空间内, 利用反射边界技术来求解相应子空间的最优控制策略; 最后根据最优控制策略的结构特性, 采用统计预测方法来预测出整个状态空间的最优控制策略. 该方法能有效降低求解涉及大状态空间及多维变量的线性混杂切换系统优化控制的计算复杂性, 文末的仿真结果验证了方法的有效性.     

A Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets

Markov chain Monte Carlo (MCMC) techniques revolutionized statistical practice in the 1990s by providing an essential toolkit for making the rigor and flexibility of Bayesian analysis computationally practical. At the same time the increasing prevalence of massive datasets and the expansion of the field of data mining has created the need for statistically sound methods that scale to these large problems. Except for the most trivial examples, current MCMC methods require a complete scan of the dataset for each iteration eliminating their candidacy as feasible data mining techniques.In this article we present a method for making Bayesian analysis of massive datasets computationally feasible. The algorithm simulates from a posterior distribution that conditions on a smaller, more manageable portion of the dataset. The remainder of the dataset may be incorporated by reweighting the initial draws using importance sampling. Computation of the importance weights requires a single scan of the remaining observations. While importance sampling increases efficiency in data access, it comes at the expense of estimation efficiency. A simple modification, based on the rejuvenation step used in particle filters for dynamic systems models, sidesteps the loss of efficiency with only a slight increase in the number of data accesses.To show proof-of-concept, we demonstrate the method on two examples. The first is a mixture of transition models that has been used to model web traffic and robotics. For this example we show that estimation efficiency is not affected while offering a 99% reduction in data accesses. The second example applies the method to Bayesian logistic regression and yields a 98% reduction in data accesses.     

基于蒙特卡洛小波去噪的股票投资组合风险优化研究

股票投资是我国重要的投资形式之一,但是从股票市场到投资者的个人投资决策都充斥着干扰和噪声。传统的随机矩阵理论（RMT）对证券投资组合风险优化产生了显著效果,然而RMT的去噪效果会随着组合证券数量的减少而下降,同时RMT仅仅是对证券收益协方差矩阵进行去噪,所以存在着一定局限性。从马科维茨(Markowitz)投资组合风险优化模型出发,基于小波分析视角讨论了蒙特卡洛模拟与小波去噪应用在投资组合风险优化上的可行性,并构造了蒙特卡洛小波去噪算法（MWF）。运用上海证券交易所A股股票交易数据进行实证分析,对比了传统的蒙特卡洛RMT(MKR)去噪方法、传统的RMT去噪法（LCPB、PG 和KR）以及单纯的Markowitz模型在股票投资组合上的风险优化效果。实证结果表明,蒙特卡洛小波去噪法在股票投资组合风险优化方面表现更好,并提供了一种新的股票投资组合配置方式。     

Progressive Latin Hypercube Sampling: An efficient approach for robust sampling-based analysis of environmental models

Efficient sampling strategies that scale with the size of the problem, computational budget, and users’ needs are essential for various sampling-based analyses, such as sensitivity and uncertainty analysis. In this study, we propose a new strategy, called Progressive Latin Hypercube Sampling (PLHS), which sequentially generates sample points while progressively preserving the distributional properties of interest (Latin hypercube properties, space-filling, etc.), as the sample size grows. Unlike Latin hypercube sampling, PLHS generates a series of smaller sub-sets (slices) such that (1) the first slice is Latin hypercube, (2) the progressive union of slices remains Latin hypercube and achieves maximum stratification in any one-dimensional projection, and as such (3) the entire sample set is Latin hypercube. The performance of PLHS is compared with benchmark sampling strategies across multiple case studies for Monte Carlo simulation, sensitivity and uncertainty analysis. Our results indicate that PLHS leads to improved efficiency, convergence, and robustness of sampling-based analyses.     

PWM控制方法用于过程控制的问题研究

PWM控制技术在电力电子技术领域得到了广泛的应用,在过程控制领域,PWM控制方式也具有特殊的优势。本文利用MATLAB仿真技术对采用PWM控制方式的控制系统进行了研究。研究的被控对象为过程控制中常见的一阶惯性和二阶惯性。本文中给出了部分的仿真图形和数据,研究的结果表明当PWM信号的周期与被控对象大时间常数的比值T/T0在0.1～0.2之间时,PWM控制的各项性能指标都比较合适。并且随着T/T0的增大,系统的超调、调节时间、稳态误差以及纹波将逐渐变大。     

Assessing the Impact of Operating Constraints and Operating Policy on the Reliability Level of a Generation System

This paper presents a chronological stochastic method for evaluating the reliability of a generation system, taking operating considerations into account. A sequential Monte Carlo production simulation is used to evaluate the risk level associated with the chronological operation of the system over a year. The approach is based on a combination of a weekly deterministic unit commitment and an hour-by-hour simulation of the system response to unit outages that are not yet known at the beginning of the week. It enables to deal with important aspects in actual system operation: time dependent constraints, energy limited units and start-up delays of thermal units. It can be used to assess the influence of the operating constraints and the operating policy on the reliability level of a generation system. The method is applied to a test case related to a single system and extended to a second text case involving two interconnected systems sharing their operating reserve.     

面向钢铁企业氧氮动态平衡的优化控制策略

钢厂氧氮使用量随钢铁生产过程节奏变化而不同,需要依靠生产调度来保持制氧和冶金工序之间的氧氮产耗平衡,然而要准确地达到动态供需平衡并不容易,氧氮管网压力的波动可以较好地体现供需平衡变化。本文将过程机理与数理统计相结合,建立钢铁生产过程的氧氮产耗预测模型和氧氮管网模拟模型,实现氧氮系统负荷变化的准确预测,进而通过先进控制、自动变负荷、自动变工况、多目标优化等技术,按各空分装置的能力和效率合理调整生产负荷,在保证产品纯度合格的前提下,快速地自动变负荷或变工况,最终实现钢厂氧氮系统的“定量调度”和“事前调度”,避免出现氧气放散和供气不足,降低生产成本。     

An Information Theory Framework for the Analysis of Scene Complexity

In this paper we present a new framework for the analysis of scene visibility and radiosity complexity. We introduce a number of complexity measures from information theory quantifying how difficult it is to compute with accuracy the visibility and radiosity in a scene. We define the continuous mutual information as a complexity measure of a scene, independent of whatever discretisation, and discrete mutual information as the complexity of a discretised scene. Mutual information can be understood as the degree of correlation or dependence between all the points or patches of a scene. Thus, low complexity corresponds to low correlation and vice versa. Experiments illustrating that the best mesh of a given scene among a number of alternatives corresponds to the one with the highest discrete mutual information, indicate the feasibility of the approach. Unlike continuous mutual information, which is very cheap to compute, the computation of discrete mutual information can however be quite demanding. We will develop cheap complexity measure estimates and derive practical algorithms from this framework in future work.     

运用CrystalBall＆ MS Project实现项目进度的蒙特卡洛风险分析

通过运用CrystalBall和MSProject软件进行蒙特卡洛模拟,对项目进度计划风险分析及实际应用进行研究和探讨,在项目管理实践中将起到非常大的作用。