Computation of risk measures in finance and parallel real-time scheduling

Many application areas employ various risk measures, such as a quantile, to assess risks. For example, in finance, risk managers employ a quantile to help determine appropriate levels of capital needed to be able to absorb (with high probability) large unexpected losses in credit portfolios comprising loans, bonds, and other financial instruments subject to default. This dissertation discusses the computation of risk measures in finance and parallel real-time scheduling. Firstly, two estimation approaches are compared for one risk measure, a quantile, via randomized quasi-Monte Carlo (RQMC) in an asymptotic setting where the number of randomizations for RQMC grows large, but the size of the low-discrepancy point set remains fixed. In the first method, for each randomization, it computes an estimator of the cumulative distribution function (CDF), which is inverted to obtain a quantile estimator, and the overall quantile estimator is the sample average of the quantile estimators across randomizations. The second approach instead computes a single quantile estimator by inverting one CDF estimator across all randomizations. Because quantile estimators are generally biased, the first method leads to an estimator that does not converge to the true quantile as the number of randomizations goes to infinity. In contrast, the second estimator does, and a central limit theorem is established for it. To get an improvement, we use conditional Monte Carlo (CMC) to obtain a smoother estimate of the distribution function, and we combine this with the second RQMC to further reduce the variance. The result is a much more accurate quantile estimator, whose mean square error can converge even faster than the canonical rate of O(1/n). Secondly, another risk measure is estimated, namely economic capital (EC), which is defined as the difference between a quantile and the mean of the loss distribution, given a stochastic model for a portfolio’s loss over a given time horizon. This work applies measure-specific importance sampling to separately estimate the two components of the EC, which can lead to a much smaller variance than when estimating both terms simultaneously. Finally, for parallel real-time tasks, the federated scheduling paradigm, which assigns each parallel task a set of dedicated cores, achieves good theoretical bounds by ensuring exclusive use of processing resources to reduce interferences. However, because cores share the last-level cache and memory bandwidth resources, in practice tasks may still interfere with each other despite executing on dedicated cores. To tackle this issue, this work presents a holistic resource allocation framework for parallel real-time tasks under federated scheduling. Under the proposed framework, in addition to dedicated cores, each parallel task is also assigned with dedicated cache and memory bandwidth resources. This work also shows the study of the characteristics of parallel tasks upon different resource allocations following a measurement-based approach and proposes a technique to handle the challenge of tremendous profiling for all resource allocation combinations under this approach. Further, it proposes a holistic resource allocation algorithm that well balances the allocation between different resources to achieve good schedulability. Additionally, this work provides a full implementation of the framework by extending the federated scheduling system with Intel’s Cache Allocation Technology and MemGuard. It also demonstrates the practicality of the proposed framework via extensive numerical evaluations and empirical experiments using real benchmark programs. In the end, the discussion about the application of risk measures for real-time scheduling is given for future work

A statistical approach to the inverse problem in magnetoencephalography

Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse problem, identifying the location of the electrical sources from the magnetic signal measurements, is ill-posed, that is, there are an infinite number of mathematically correct solutions. Common source localization methods assume the source does not vary with time and do not provide estimates of the variability of the fitted model. Here, we reformulate the MEG inverse problem by considering time-varying locations for the sources and their electrical moments and we model their time evolution using a state space model. Based on our predictive model, we investigate the inverse problem by finding the posterior source distribution given the multiple channels of observations at each time rather than fitting fixed source parameters. Our new model is more realistic than common models and allows us to estimate the variation of the strength, orientation and position. We propose two new Monte Carlo methods based on sequential importance sampling. Unlike the usual MCMC sampling scheme, our new methods work in this situation without needing to tune a high-dimensional transition kernel which has a very high cost. The dimensionality of the unknown parameters is extremely large and the size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed up the computation.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS716 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parallel detrended fluctuation analysis for fast event detection on massive PMU data

("(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.")Phasor measurement units (PMUs) are being rapidly deployed in power grids due to their high sampling rates and synchronized measurements. The devices high data reporting rates present major computational challenges in the requirement to process potentially massive volumes of data, in addition to new issues surrounding data storage. Fast algorithms capable of processing massive volumes of data are now required in the field of power systems. This paper presents a novel parallel detrended fluctuation analysis (PDFA) approach for fast event detection on massive volumes of PMU data, taking advantage of a cluster computing platform. The PDFA algorithm is evaluated using data from installed PMUs on the transmission system of Great Britain from the aspects of speedup, scalability, and accuracy. The speedup of the PDFA in computation is initially analyzed through Amdahl's Law. A revision to the law is then proposed, suggesting enhancements to its capability to analyze the performance gain in computation when parallelizing data intensive applications in a cluster computing environment

Miniaturized modular manipulator design for high precision assembly and manipulation tasks

In this paper, design and control issues for the development of miniaturized manipulators which are aimed to be used in high precision assembly and manipulation tasks are presented. The developed manipulators are size adapted devices, miniaturized versions of conventional robots based on well-known kinematic structures. 3 degrees of freedom (DOF) delta robot and a 2 DOF pantograph mechanism enhanced with a rotational axis at the tip and a Z axis actuating the whole mechanism are given as examples of study. These parallel mechanisms are designed and developed to be used in modular assembly systems for the realization of high precision assembly and manipulation tasks. In that sense, modularity is addressed as an important design consideration. The design procedures are given in details in order to provide solutions for miniaturization and experimental results are given to show the achieved performances