Valuation of R&;D Sequential Exchange Options Using Monte Carlo Approach

This article describes a methodology for evaluating R&D investment projects using Monte Carlo method. R&D projects generally involve multiple phases with or without overlapping. R&D investments are made often in a phased manner, with the commencement of subsequent phase being dependent on the successful completion of the preceding phase. This is known as sequential investment. Moreover, each stage creates an opportunity (option) for subsequent investment. Therefore, R&D projects can be considered as ‘Compound Options’ in which investments present uncertainty both in the gross project value and in their costs. It is possible to use exchange options to value the R&D investment opportunities. In this paper, we propose to evaluate the European and American Real Compound exchange options through Monte Carlo simulations. We also provide a set of numerical experiments to provide evidence for the accuracy of the proposed methodology.      

鲁棒的机器人蒙特卡洛定位算法

提出一种基于粒子滤波器的机器人定位算法. 首先利用一并行扩展卡尔曼滤波器作为粒子预测分布, 将当前观测的部分信息融入, 以改善滤波效果, 减小所需粒子数; 然后提出变密度函数边界的马尔可夫链蒙特卡洛(Markov chain Monte Carlo, MCMC)重采样方法, 以提高粒子的细化能力; 最后结合普通重采样方法, 提出一种改进的MCMC重采样的机器人定位算法, 减少粒子匮乏效应的同时, 提高了定位精度. 实验结果表明, 该算法较传统方法在计算复杂度、定位精度和鲁棒性方面都有显著提高.     

Valuation of R&D Investment Opportunities with the Threat of Competitors Entry in Real Option Analysis

This paper provides a real option methodology in order to value a pioneer’s R&D investment opportunity allowing for more potential competitors to enter in the market. To incorporate this competitive dimension, we assume that the pioneer may lose the “competitive dividends”   if the real option is not exercised. According to Majd and pindyck (1987) (Journal of Financial Economics 18(1):7–27), in a real options context, “dividends”   are the opportunity costs inherent in the decision to defer an investment project and so deferment implies the loss of project’s cash flows. Concerning this, Trigeorgis (1996) (Real Options: Managerial Flexibility and Strategy in Resource Allocation, The MIT Press, Cambridge, (1996) incorporates the preemption effect through the “competitive dividends”  which are the cash flows that can be eroded by anticipated competitive arrivals. In particular way, we propose the valuation of a pioneer’s R&D investment assuming that the Development cost can be spent in two moments: $t_2$ or $t_3$ . If the Development cost is realized in $t_2$ no firms enters in the market since the rivals’ R&D plan is not yet concluded otherwise, if the Development cost is delayed until time $t_3$ waiting better market conditions, other rivals may enter in the market and so the opportunity costs, namely dividends, increase. Moreover, we analyze the optimal timing to realize the Development investment, i.e. we determine the conditions for which the pioneer prefers to invest the Development cost at time $t_2$ or $t_3$ .     

基于序列蒙特卡罗方法的3D人体运动跟踪

针对人体运动跟踪的特点,在退火粒子滤波方法的基础上,提出基于序列蒙特卡罗方法的3D人体跟踪算法．通过状态空间分解提高了退火系数选择的鲁棒性;同时,在每次退火时采用PERM采样方法,而不是标准的重采样,能在一定程度上抑制观测模型与真实分布之间的误差,从而提高算法的稳定性．通过模拟实验表明,该算法适合3D多关节人体跟踪．     

General and Robust Error Estimation and Reconstruction for Monte Carlo Rendering

Adaptive filtering techniques have proven successful in handling non‐uniform noise in Monte‐Carlo rendering approaches. A recent trend is to choose an optimal filter per pixel from a selection of non spatially‐varying filters. Nonetheless, the best filter choice is difficult to predict in the absence of a reference rendering. Our approach relies on the observation that the reconstruction error is locally smooth for a given filter. Hence, we propose to construct a dense error prediction from a small set of sparse but robust estimates. The filter selection is then formulated as a non‐local optimization problem, which we solve via graph cuts, to avoid visual artifacts due to inconsistent filter choices. Our approach does not impose any restrictions on the used filters, outperforms previous state‐of‐the‐art techniques and provides an extensible framework for future reconstruction techniques.     

An R&D Investment Game under Uncertainty in Real Option Analysis

One of the problems of using the financial options methodology to analyse investment decisions is that strategic considerations become extremely important. So, the theory of real option games combines two successful theories, namely real options and game theory. The investment opportunity and the value of flexibility can be valued as a real option while the competition can be analyzed with game theory. In our model we develop an interaction between two firms that invest in R&D. The firm that invests first, defined as the Leader, acquires a first mover advantage that we assume as a higher share of market. But, several R&D investments present positive externalities and so, the option exercise by the Leader generates an “Information-Revelation”, that benefits the Follower.     

Robust particle tracker via Markov Chain Monte Carlo posterior sampling

Particle Filter has grown to be a standard framework for visual tracking. This paper proposes a robust particle tracker based on Markov Chain Monte Carlo method, aiming at solving the thorny problems in visual tracking induced by object appearance changes, occlusions, background clutter, and abrupt motions. In this algorithm, we derive the posterior probability density function based on second order Markov assumption. The posterior probability density is the joint density of the previous two states. Additionally, a Markov Chain with certain length is used to approximate the posterior density to avoid the drawbacks of traditional importance sampling based algorithm, which consequently improves the searching ability of the proposed tracker. We compare our approach with several alternative tracking algorithms, and the experimental results demonstrate that our tracker is superior to others in dealing with various types of challenging scenarios.     

Robust Image Denoising Using a Virtual Flash Image for Monte Carlo Ray Tracing

We propose an efficient and robust image‐space denoising method for noisy images generated by Monte Carlo ray tracing methods. Our method is based on two new concepts: virtual flash images and homogeneous pixels. Inspired by recent developments in flash photography, virtual flash images emulate photographs taken with a flash, to capture various features of rendered images without taking additional samples. Using a virtual flash image as an edge‐stopping function, our method can preserve image features that were not captured well only by existing edge‐stopping functions such as normals and depth values. While denoising each pixel, we consider only homogeneous pixels—pixels that are statistically equivalent to each other. This makes it possible to define a stochastic error bound of our method, and this bound goes to zero as the number of ray samples goes to infinity, irrespective of denoising parameters. To highlight the benefits of our method, we apply our method to two Monte Carlo ray tracing methods, photon mapping and path tracing, with various input scenes. We demonstrate that using virtual flash images and homogeneous pixels with a standard denoising method outperforms state‐of‐the‐art image‐space denoising methods.     

蒙特卡洛方法在仿真中的应用

本文介绍了蒙特卡洛方法,一种利用随机数(或伪随机数)来解决许多类型计算问题的通用算法。首先描述了蒙特卡洛方法的基本原理,并且通过两个典型应用案例,讨论了蒙特卡洛方法的适用范围和使用条件,展示了该方法的优点,体现了该方法在解决高自由度问题方面的优势。     

纵向研发合作的研发绩效和成本分担机制

在日益激烈的市场竞争环境下,企业往往会选择研发合作以降低研发的成本和风险,而纵向研发合作已成为其中的重要模式。构建了一个存在两个上游企业和多个下游企业所组成的复杂双层市场结构,对上下游企业实施纵向研发合作的产量变化和利润变化进行了分析,在此基础上探讨了研发合作的最优研发绩效。研究了纵向研发合作下利润匹配型和固定比例型两种分担机制的分担系数和净利润等经济指标,得出了一些符合现实经济活动的结论。     

基于Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪

在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC（Markov chain Monte Carlo）算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.     

An object-oriented Monte Carlo simulator for 3D cylindrical positron tomographs

Monte Carlo simulation is a very powerful tool in understanding performances of positron tomographs as well as in assessing image reconstruction algorithms and their implementations. We present an object-oriented Monte Carlo simulator developed for 3D positron tomography. Results from phantom simulation studies including absorption and scattering of the photons in the field-of-view are presented. Scatter fractions determined from these studies are in good agreement with measured scatter fractions published in the literature. Limitations and future prospects are discussed.     

Monte Carlo algorithms for evaluating Sobol’ sensitivity indices

Sensitivity analysis is a powerful technique used to determine robustness, reliability and efficiency of a model. The main problem in this procedure is the evaluating total sensitivity indices that measure a parameter’s main effect and all the interactions involving that parameter. From a mathematical point of view this problem is presented by a set of multidimensional integrals. In this work a simple adaptive Monte Carlo technique for evaluating Sobol’ sensitivity indices is developed. A comparison of accuracy and complexity of plain Monte Carlo and adaptive Monte Carlo algorithms is presented. Numerical experiments for evaluating integrals of different dimensions are performed.     

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.     

蒙特卡罗方法在教学中的应用

介绍了蒙特卡罗方法在教学中的应用,给出了两个实例.     

一种估计网络可靠性的蒙特卡洛方法

将K—终端剩余连通可靠度的概念推广到链路存在失效状态的网络模型上,并提出了计算该可靠度的基于RVR的蒙特卡洛方法。首先对网络链路的状态进行抽样。在网络所有链路状态确定的前提下计算网络的K—终端剩余连通可靠度,即等价于计算相同拓扑结构,链路完全可靠网络的K—终端剩余连通可靠度,对于后者可采用H.Cancela等提出的基于RVR的蒙特卡洛算法。实践证明该估计方法是无偏的,且与原始的蒙特卡洛方法相比具有较小的方差。