基于GPU的最小二乘蒙特卡罗算法期权定价

期权是以金融产品作为行权品种的交易合约。随着期权交易规模和交易量的迅速增长,期权定价的计算量越来越大,在传统CPU平台上对期权进行定价变得越来越困难。图形处理器（GPU）平台的出现和发展为解决期权定价计算提供了解决方案。在GPU上使用最小二乘蒙特卡罗算法（Least Squares Monte Carlo,LSM）实现了对一维和四维美式期权定价计算：首先利用CURAND库产生大量随机数,然后并行化期权标的价格变化路径,最后对最小二乘法和贴现定价进行并行化。为提高GPU平台上LSM方法的计算效率,对整个过程进行了优化。实际测试结果表明,在CPU+GPU上实现一维和四维美式期权定价相对CPU平台的加速比最高分别达到20.275和47.538,且比其他文献的方法整体性能有较大的提升。     

基于特征粒子的Monte Carlo自定位方法

提出了一种基于Monte Carlo方法的多机器人自定位方法．该方法在机器人进行自定位时，对用来估计机器人位置的MCL(Monte Carlo Localization)粒子空间进行栅格划分，然后采用可变栅格法获得能代表所有粒子整体特性的特征粒子集．因为特征粒子的数量较粒子总数大大减少，该方法能避免直接将Monte Carlo方法应用于多机器人定位中产生的维数灾的问题，可以在保证精度的情况下降低运算复杂度．仿真结果表明，该方法能较好地满足多机器人自定位的要求．     

有色噪声下自校正控制器的Monte Carlo仿真研究

本文首次将 Monte Carlo 随机模拟法引入到极点配置自校正控制器的研究和设计中.讨论了面向真实有色噪声环境的自校正控制器的一般设计方案,作为一个应用实例,完成了船舶自校正控制器的 Monte Carlo 仿真研究.     

数字通信系统中的Monte Carlo仿真

介绍数字通信系统的广泛应用和Monte Carlo算法的基本思想,重点分析数字通信系统中的差错概率和应用Monte Carlo仿真对存在噪声和干扰的数字通信系统的性能进行评估。     

随机网格回归Monte Carlo双UAVs最优目标协调跟踪

针对多个无人机(unmanned aerial vehicle,UAV)执行基于视觉的目标跟踪的最佳协调问题,提高不可预知的地面目标的最佳结合点的视觉测量效果,提出了一种基于随机网格回归Monte Carlo的UAV最优目标跟踪策略。首先,通过无人机动力学和目标动力学分析,获得双UAV情况下的随机最优协调控制目标;其次,针对提出的控制目标,引入Monte Carlo求解方案,同时为解决标准Monte Carlo方案中存在的状态空间维度较高,计算复杂且精度不高的问题,利用随机网格方式构建回归Monte Carlo方案,实现UAV的最优协调控制;最后,通过仿真实验验证了所提方法的有效性。     

改进Monte Carlo算法用于RFID标签的室内定位

针对基于信号到达时间延迟(TOA)的定位算法存在的问题,改进了基于采样的Monte Carlo定位算法.将其用于室内射频标签的定位,分析了天线极化失配对改进的Monte Carlo定位算法的影响.仿真结果表明,改进的Monte Carlo定位算法受天线极化失配的影响较大,定位误差随标签与读写器天线之间极化方向的夹角的增大而增大.     

基于Monte-Carlo方法的井下无线传感网络定位算法

在无线传感器网络应用当中,位置数据向来是关键信息之一。怎样用最小的代价,使得定位算法更加稳定健壮、更精确、更高效,是目前无线传感网定位算法追求的一个方向。因为无线传感网络有着很强的应用相关性,Monte—Carlo中心定位算法以井下环境为背景,设计的一种基于Monte—Carlo算法的改进的定位算法,定位方法简单,定位计算量小。最后通过实验将该算法和Monte．Carlo算法进行了仿真,结果显示在井下环境条件下,该算法有很强的稳定性和更好的精度。     

序贯Monte Carlo算法仿真结果分析

序贯Monte Carlo方法能够解决很多实际问题.它的系统模型与Kalman滤波算法相比具有更广泛的适用性,所以研究Monte Carlo方法是很有实际意义的.文中对序贯Monte Carlo算法进行性能分析,对这一方法的跟踪能力进行了仿真实验.采用的仿真系统模型是非线性系统模型.仿真实验比较了EKF、SIS、SIR算法的性能.通过对不同算法的仿真结果之间的分析和比较,得出了有意义的结论.这对一些工程问题的解决是有重要意义的.     

智能空间辅助家庭服务机器人的定位方法

研究移动机器人智能定位优化问题,在分析传统的移动机器人定位的过程中,由于在定位时存在误匹配造成不准确,传统的移动机器人自身携带传感器对周围环境观测具有局限性.为了提高有效定位,提出利用智能空间中的单个全局摄像机作为外部传感器,可采用Monte Carlo方法解决移动机器人定位,并进行仿真,实验表明,全局摄像机能够有效地辅助移动机器人在全局环境中定位,Monte Carlo算法利用全局摄像机的观测信息,使定位有良好的性能效果.     

混沌优化算法的性能分析

现代优化算法主要解决全局最优问题，其本质是概率性的．借鉴多种自然现象，人们提出了许多仿生、仿物算法，如禁忌搜索算法（TABU）、模拟退火（SAA）、遗传算法（GA）、进化策略（ES）、蚁群算法（ACA）等．利用混沌的遍历性进行优化搜索就是一种很有趣的研究思路，尤其对于虫口方程人们进行了许多研究，取得了一定的研究成果．但和普通的随机搜索算法相比，其性能之不足也很明显，主要体现在：混沌的遍历性不均匀，在边界处搜索密度高，远不如随机Monte Carlo搜索方法．这就从本质上决定了其搜索性能在普适性上与Monte Carlo算法有差距．仿真计算证实了这个结论．因此对于利用虫口方程进行的混沌优化研究需要谨慎采用．     

基于SOA金融仿真平台的研究与实践

面对日益复杂的金融仿真要求,为了提高仿真准确性,满足实时性需求,通过实现面向服务架构的金融仿真平台,减低仿真平台的耦合性,同时提供金融仿真实践中常用的蒙特卡洛数值计算框架,采用简化仿真模型的建立过程来减低成本.在此基础上通过股票价格行为模型和期权定价模型对仿真平台性能进行测试,结果与实际数据对比,结果稳定,误差率低.由此表明仿真平台能够满足实际金融仿真的需求.     

Monte Carlo implementation of financial simulation on Cell/B.E. multi-core processor

The processor evolution has reached a critical moment in time where it will soon be impossible to increase the frequency much further. Processor designers such as Motorola, Intel and IBM have all realised that the only way to improve the FLOP/Watt ratio is to develop multi-core devices. One of the most current examples of multi-core processors is the new Sony/Toshiba/IBM Cell/B.E. multi-core processor. For the suitability to run in parallel, Monte Carlo methods are often considered embarrassingly parallel. This paper describes how a common Monte Carlo based financial simulation can be calculated in parallel using the Cell/B.E. multi-core processor. The measured performance with the achieved multi-core speed-up is also presented. With the recent availability of this increasingly available technology, financial simulations can now be performed in a fraction of the time it used to. This can also be achieved with a limited power and volume budget using commercially available technology. The main challenge with multi-core devices is clearly the programmability. The work presented here describes how this challenge could be dealt with.A basic MPI library has been developed to handle the partitioning and communication of data. The thread creation follows a POSIX thread creation model. MPI together with POSIX make the application portable in between various multi-processor systems and multi-core devices. The conclusions made indicate that a function offload MPI implementation on the Cell/B.E. multi-core processor can efficiently be used to speed-up the Monte Carlo solution of financial simulations. The conclusions made herein are also applicable to other situations where an algorithm can be easily parallelized.     

The equivalent martingale measure: an introduction to pricing usingexpectations

We provide a self contained introduction to the risk neutral or martingale approach to the pricing of financial derivatives, while assuming no financial background. This approach to pricing provides a rich source of problems ideally suited to the application of Monte Carlo methods, thus forming a bridge between computational finance and some of the well developed tools available to engineers and scientists. We illustrate the power of the martingale approach by using it to develop the price of the European call option using only elementary methods and briefly discuss the pricing of the American put option as well as interest rate derivatives.     

High-performance computing in finance: The last 10 years and the next

Almost two decades ago supercomputers and massively parallel computers promised to revolutionize the landscape of large-scale computing and provide breakthrough solutions in several application domains. Massively parallel processors achieve today terraFLOPS performance – trillion floating point operations per second – and they deliver on their promise. However, the anticipated breakthroughs in application domains have been more subtle and gradual. They came about as a result of combined efforts with novel modeling techniques, algorithmic developments based on innovative mathematical theories, and the use of high-performance computers that vary from top-range workstations, to distributed networks of heterogeneous processors, and to massively parallel computers. An application that benefited substantially from high-performance computing is that of finance and financial planning. The advent of supercomputing coincided with the so-called “age of the quants” in Wall Street, i.e., the mathematization of problems in finance and the strong reliance of financial managers on quantitative analysts. These scientists, aided by mathematical models and computer simulations, aim at a better understanding of the peculiarities of the financial markets and the development of models that deal proactively with the uncertainties prevalent in these markets. In this paper we give a modest synthesis of the developments of high-performance computing in finance. We focus on three major developments: (1) The use of Monte Carlo simulation methods for security pricing and Value-at-Risk (VaR) calculations; (2) the development of integrated financial product management tools and practices – also known as integrative risks management or enterprise-wide risk management, and (3) financial innovation and the computer-aided design of financial products.     

面向多智能体博弈的并行蒙特卡洛树搜索算法研究

蒙特卡洛树搜索算法是一种常用的强化学习算法,博弈过程中动态空间的指数级增长是制约该算法学习效率的因素。基于并行方法对蒙特卡洛树搜索算法进行优化,提出基于胜率估值传递的并行蒙特卡洛树搜索算法。改进后的并行博弈搜索策略框架包含一个主进程和多个子进程,其中子进程用于探索,主进程根据子进程传递的胜率估值数据进行决策。结合多智能体博弈平台Pommerman进行实验验证,与传统的蒙特卡罗树搜索算法相比,并行蒙特卡罗树搜索算法有效提高了资源利用率、博弈胜率及决策效率。      

Parallel tempering simulation of the three-dimensional Edwards–Anderson model with compact asynchronous multispin coding on GPU

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional 28.4% speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 ps per spin flip attempt for simulating the three-dimensional Edwards–Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.     

基于蒙特卡罗模拟修正的随机矩阵去噪方法

针对蕴含噪声信息较少的小组合股票市场,提出使用蒙特卡罗模拟修正的随机矩阵去噪方法。首先通过数据模拟生成随机矩阵,然后利用大量的模拟数据来同时修正噪声下界和上界,最终对噪声范围进行精确测定。运用道琼斯中国88指数和香港恒生50指数的数据进行实证分析,结果表明,与LCPB法、PG+法和KR法相比,在特征值、特征向量和反比参率方面, 蒙特卡罗模拟去噪方法修正后噪声范围的合理性及有效性得到很大的提升;对去噪前后的相关矩阵进行投资组合,得知在相同的期望收益率下,蒙特卡罗模拟去噪方法具有最小的风险值,能够为资产组合选择和风险管理等金融应用提供一定的参考。     

Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel

Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as “embarrassingly parallel”, meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.     

GPU acceleration of the stochastic grid bundling method for early-exercise options

In this work, a parallel graphics processing units (GPU) version of the Monte Carlo stochastic grid bundling method (SGBM) for pricing multi-dimensional early-exercise options is presented. To extend the method's applicability, the problem dimensions and the number of bundles will be increased drastically. This makes SGBM very expensive in terms of computational costs on conventional hardware systems based on central processing units. A parallelization strategy of the method is developed and the general purpose computing on graphics processing units paradigm is used to reduce the execution time. An improved technique for bundling asset paths, which is more efficient on parallel hardware is introduced. Thanks to the performance of the GPU version of SGBM, a general approach for computing the early-exercise policy is proposed. Comparisons between sequential and GPU parallel versions are presented.