Download or read book Sparse Optimization Methods and Statistical Modeling with Applications to Finance written by Michael Ho and published by . This book was released on 2016 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this dissertation we examine methods to address this problem through application of methods and techniques from sparse optimization and modeling. Two new techniques are developed with the aim of improving the performance of mean-variance portfolio optimization.In the first technique a pairwise weighted elastic net penalized mean-variance criterion for portfolio design in proposed. Here we motivate the use of this penalty through a robust optimization interpretation. This interpretation is then employed to develop a bootstrap calibration technique for the pairwise elastic net. The benefit of the pairwise weighted elastic net and calibration is shown in portfolio performance results using recent U.S. stock market data.In the second application robust Kalman filtering techniques are applied to return covariance estimation from high frequency financial price data. The methods developed address three factors which make covariance estimation from high frequency data difficult: 1) microstructure noise, 2) asynchronous trading, and 3) jumps. The performance of these robust Kalman filtering techniques are tested against simulated high frequency data and are compared with other existing covariance estimators. The results indicate that the robust Kalman filtering techniques substantially improve covariance estimation performance versus other approaches.

Download or read book Statistical Models and Methods for Financial Markets written by Tze Leung Lai and published by Springer Science & Business Media. This book was released on 2008-07-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of writing this bookarosein 2000when the ?rst author wasassigned to teach the required course STATS 240 (Statistical Methods in Finance) in the new M. S. program in ?nancial mathematics at Stanford, which is an interdisciplinary program that aims to provide a master’s-level education in applied mathematics, statistics, computing, ?nance, and economics. Students in the programhad di?erent backgroundsin statistics. Some had only taken a basic course in statistical inference, while others had taken a broad spectrum of M. S. - and Ph. D. -level statistics courses. On the other hand, all of them had already taken required core courses in investment theory and derivative pricing, and STATS 240 was supposed to link the theory and pricing formulas to real-world data and pricing or investment strategies. Besides students in theprogram,thecoursealso attractedmanystudentsfromother departments in the university, further increasing the heterogeneity of students, as many of them had a strong background in mathematical and statistical modeling from the mathematical, physical, and engineering sciences but no previous experience in ?nance. To address the diversity in background but common strong interest in the subject and in a potential career as a “quant” in the ?nancialindustry,thecoursematerialwascarefullychosennotonlytopresent basic statistical methods of importance to quantitative ?nance but also to summarize domain knowledge in ?nance and show how it can be combined with statistical modeling in ?nancial analysis and decision making. The course material evolved over the years, especially after the second author helped as the head TA during the years 2004 and 2005.

Download or read book Sparse Optimization Theory and Methods written by Yun-Bin Zhao and published by CRC Press. This book was released on 2018-07-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.

Download or read book Modeling and Optimization Theory and Applications written by János D. Pintér and published by Springer. This book was released on 2019-02-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in B ethlehem, Pennsylvania, USA between August 16-18, 2017. The conference brought together a diverse group of researchers and practitioners working on both theoretical and practical aspects of continuous and discrete optimization. Topics covered include algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and address the application of deterministic andstochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The selected contributions in this book illustrate the broad diversity of ideas discussed at the meeting.

Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Download or read book Convex Optimization Methods for Graphs and Statistical Modeling written by Venkat Chandrasekaran and published by . This book was released on 2011 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: An outstanding challenge in many problems throughout science and engineering is to succinctly characterize the relationships among a large number of interacting entities. Models based on graphs form one major thrust in this thesis, as graphs often provide a concise representation of the interactions among a large set of variables. A second major emphasis of this thesis are classes of structured models that satisfy certain algebraic constraints. The common theme underlying these approaches is the development of computational methods based on convex optimization, which are in turn useful in a broad array of problems in signal processing and machine learning. The specific contributions are as follows: -- We propose a convex optimization method for decomposing the sum of a sparse matrix and a low-rank matrix into the individual components. Based on new rank-sparsity uncertainty principles, we give conditions under which the convex program exactly recovers the underlying components. -- Building on the previous point, we describe a convex optimization approach to latent variable Gaussian graphical model selection. We provide theoretical guarantees of the statistical consistency of this convex program in the high-dimensional scaling regime in which the number of latent/observed variables grows with the number of samples of the observed variables. The algebraic varieties of sparse and low-rank matrices play a prominent role in this analysis. -- We present a general convex optimization formulation for linear inverse problems, in which we have limited measurements in the form of linear functionals of a signal or model of interest. When these underlying models have algebraic structure, the resulting convex programs can be solved exactly or approximately via semidefinite programming. We provide sharp estimates (based on computing certain Gaussian statistics related to the underlying model geometry) of the number of generic linear measurements required for exact and robust recovery in a variety of settings. -- We present convex graph invariants, which are invariants of a graph that are convex functions of the underlying adjacency matrix. Graph invariants characterize structural properties of a graph that do not depend on the labeling of the nodes; convex graph invariants constitute an important subclass, and they provide a systematic and unified computational framework based on convex optimization for solving a number of interesting graph problems. We emphasize a unified view of the underlying convex geometry common to these different frameworks. We describe applications of both these methods to problems in financial modeling and network analysis, and conclude with a discussion of directions for future research.

Download or read book Optimization Methods in Finance written by Gérard Cornuéjols and published by Cambridge University Press. This book was released on 2018-08-09 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and additional material to highlight the relevance to finance.

Download or read book Introduction to Optimization Methods and their Application in Statistics written by B. Everitt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization techniques are used to find the values of a set of parameters which maximize or minimize some objective function of interest. Such methods have become of great importance in statistics for estimation, model fitting, etc. This text attempts to give a brief introduction to optimization methods and their use in several important areas of statistics. It does not pretend to provide either a complete treatment of optimization techniques or a comprehensive review of their application in statistics; such a review would, of course, require a volume several orders of magnitude larger than this since almost every issue of every statistics journal contains one or other paper which involves the application of an optimization method. It is hoped that the text will be useful to students on applied statistics courses and to researchers needing to use optimization techniques in a statistical context. Lastly, my thanks are due to Bertha Lakey for typing the manuscript.

Download or read book Numerical Methods and Optimization in Finance written by Manfred Gilli and published by Academic Press. This book was released on 2011-07-11 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Download or read book Introduction to Statistical Methods for Financial Models written by Thomas A Severini and published by CRC Press. This book was released on 2017-07-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the use of statistical concepts and methods to model and analyze financial data. The ten chapters of the book fall naturally into three sections. Chapters 1 to 3 cover some basic concepts of finance, focusing on the properties of returns on an asset. Chapters 4 through 6 cover aspects of portfolio theory and the methods of estimation needed to implement that theory. The remainder of the book, Chapters 7 through 10, discusses several models for financial data, along with the implications of those models for portfolio theory and for understanding the properties of return data. The audience for the book is students majoring in Statistics and Economics as well as in quantitative fields such as Mathematics and Engineering. Readers are assumed to have some background in statistical methods along with courses in multivariate calculus and linear algebra.

Download or read book Stochastic Modeling in Economics and Finance written by Jitka Dupacova and published by Springer Science & Business Media. This book was released on 2002-08-31 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike other books that focus only on selected specific subjects this book provides both a broad and rich cross-section of contemporary approaches to stochastic modeling in finance and economics; it is decision making oriented. The material ranges from common tools to solutions of sophisticated system problems and applications. In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities. Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects. Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study. Selected examples of successful applications in finance, production planning and management of technological processes and electricity generation are presented. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories. In Part IV, the sections devoted to stochastic calculus cover also more advanced topics such as DDS Theorem or extremal martingale measures, which make it possible to treat more delicate models in Mathematical Finance (complete markets, optimal control, etc.) Audience: Students and researchers in probability and statistics, econometrics, operations research and various fields of finance, economics, engineering, and insurance.

Download or read book Modeling and Optimization Theory and Applications written by Luis F. Zuluaga and published by Springer. This book was released on 2013-11-23 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on July 30-August 1, 2012. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

Download or read book Financial Signal Processing and Machine Learning written by Ali N. Akansu and published by John Wiley & Sons. This book was released on 2016-05-31 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches. Key features: Highlights signal processing and machine learning as key approaches to quantitative finance. Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems. Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques. Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.

Download or read book Statistical Methods for Financial Engineering written by Bruno Remillard and published by CRC Press. This book was released on 2013-04-05 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: While many financial engineering books are available, the statistical aspects behind the implementation of stochastic models used in the field are often overlooked or restricted to a few well-known cases. Statistical Methods for Financial Engineering guides current and future practitioners on implementing the most useful stochastic models used in financial engineering. After introducing properties of univariate and multivariate models for asset dynamics as well as estimation techniques, the book discusses limits of the Black-Scholes model, statistical tests to verify some of its assumptions, and the challenges of dynamic hedging in discrete time. It then covers the estimation of risk and performance measures, the foundations of spot interest rate modeling, Lévy processes and their financial applications, the properties and parameter estimation of GARCH models, and the importance of dependence models in hedge fund replication and other applications. It concludes with the topic of filtering and its financial applications. This self-contained book offers a basic presentation of stochastic models and addresses issues related to their implementation in the financial industry. Each chapter introduces powerful and practical statistical tools necessary to implement the models. The author not only shows how to estimate parameters efficiently, but he also demonstrates, whenever possible, how to test the validity of the proposed models. Throughout the text, examples using MATLAB® illustrate the application of the techniques to solve real-world financial problems. MATLAB and R programs are available on the author’s website.

Download or read book Sparse Modeling written by Irina Rish and published by CRC Press. This book was released on 2014-12-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.

Download or read book Modeling and Optimization Theory and Applications written by Martin Takáč and published by Springer. This book was released on 2017-10-30 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on August 17-19, 2016. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of deterministic and stochastic optimization techniques in energy, finance, logistics, analytics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.