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。     

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     

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.     

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.     

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.     

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。     

Development and Analysis of a Multi-Wavelength Near-Infrared Sensor for Monitoring Skin Hydration and Validation Using Monte Carlo Simulation

The monitoring of an individual's hydration levels is a vital measurement required for the maintenance of a healthy skin barrier function as well as the avoidance of dehydration.The current commercial devices for this measure are typically based on electrical methodologies,such as capacitance,which allows for the extraction of skin hydration using the ionic balance deviations in the stratum corneum.The use of optical-based methods such as near-infrared spectroscopy(NIRS)has been recently explored for the measurement of skin hydration.Optical approaches have the ability to penetrate deeper into the skin layers and provide detailed information on the optical properties of present water bands.This paper presents the development of a multi-wavelength optical sensor and its capability of assessing skin hydration in an in vitro experiment utilizing porcine skin.Regression analysis of the results showed to be in line with standard reference measurements(R2CV=0.952257),validating the accuracy of the developed sensor in measuring dermal water content.A Monte Carlo model of the human skin was also developed and simulated to predict the optical sensor's performance at variable water concentrations.This model serves as a tool for validating the sensor measurement accuracy.The output from this model gave a standard expectation of the device,which agreed with trends seen in the in vitro work.This research strongly suggests that non-invasive(wearable)NIR based sensors could be used for the comprehensive assessment of skin hydration.     

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.     

Improving the state estimation for optimal control of stochastic processes subject to multiplicative noise

Computational models for the neural control of movement must take into account the properties of sensorimotor systems, including the signal-dependent intensity of the noise and the transmission delay affecting the signal conduction. For this purpose, this paper presents an algorithm for model-based control and estimation of a class of linear stochastic systems subject to multiplicative noise affecting the control and feedback signals. The state estimator based on Kalman filtering is allowed to take into account the current feedback to compute the current state estimate. The optimal feedback control process is adapted accordingly. The resulting estimation error is smaller than the estimation error obtained when the current state must be predicted based on the last feedback signal, which reduces variability of the simulated trajectories. In particular, the performance of the present algorithm is good in a range of feedback delay that is compatible with the delay induced by the neural transmission of the sensory inflow.     

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。     

内燃机缸内复杂空间三维动态网格生成技术

将组合网格拆解为静态和动态2个区域,提出了在活塞和气门运动方向上拉伸和压缩网格空间的算法．实验结果表明：3D动态网格可以应用于内燃机缸内工作过程数值模拟．     

Multiscale methods for the valuation of American options with stochastic volatility

This paper deals with the efficient valuation of American options. We adopt Heston's approach for a model of stochastic volatility, leading to a generalized Black–Scholes equation called Heston's equation. Together with appropriate boundary conditions, this can be formulated as a parabolic boundary value problem with a free boundary, the optimal exercise price of the option. For its efficient numerical solution, we employ, among other multiscale methods, a monotone multigrid method based on linear finite elements in space and display corresponding numerical experiments.     

The MISCAN simulation program for the evaluation of screening for disease

The computer program MISCAN is developed for use in evaluation of mass screening for disease. The program uses Monte Carlo simulation. It produces output on the results of screening projects and on the effects of screening on morbidity and mortality on the individual and population level. The calculations are based on models of the natural history of the disease and of the impact of screening on the natural history. The approach is such that considerable flexibility exists in specifying the structure of the model and its parameters. The program consists of two parts. The DISEASE part can be used for simulating the epidemiology of the disease when no screening is taking place; it requires input on the population and on the disease process. The SCREENING part is to be used in combination with the DISEASE part. It is intended for simulation of the results and effects of a screening project. It requires input on the properties of the screening tests, the consequences of early detection by screening, and the policy (ages and intervals between screens) of the project. MISCAN can be used for finding model assumptions regarding the disease process and the impact of screening that give a good explanation of the observed results of a screening project. Such an analysis proceeds in two steps. First, MISCAN is used to calculate simulated results of the project, based on specific assumptions. Next, these results are tested against the observed results, in order to assess the acceptability of the assumptions. MISCAN can also be used for optimization of the screening policy by simulating the cost and benefit components of a large number of different screening policies.     

A Dirichlet process mixture model for the analysis of correlated binary responses

The multivariate probit model is a popular choice for modelling correlated binary responses. It assumes an underlying multivariate normal distribution dichotomized to yield a binary response vector. Other choices for the latent distribution have been suggested, but basically all models assume homogeneity in the correlation structure across the subjects. When interest lies in the association structure, relaxing this homogeneity assumption could be useful. The latent multivariate normal model is replaced by a location and association mixture model defined by a Dirichlet process. Attention is paid to the parameterization of the covariance matrix in order to make the Bayesian computations convenient. The approach is illustrated on a simulated data set and applied to oral health data from the Signal Tandmobiel^® study to examine the hypothesis that caries is mainly a spatially local disease.