Download or read book Correcting the Monte Carlo Optimal stopping Bias written by Tyson L. Whitehead and published by . This book was released on 2008 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bias Corrected Least Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems written by Johan Andreasson and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Least-Squares Monte Carlo method has gained popularity recent years due to its ability to handle multi-dimensional stochastic control problems without restrictions on the state dynamics, including problems with state variables affected by control. However, when applied to stochastic control problems in the multiperiod expected utility models, the regression t tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of stochastic control problems to improve the regression t, and then using either the 'Smearing Estimate' or 'Controlled Heteroskedasticity' to avoid the re-transformation bias. We also present and utilise recent improvements in Least-Squares Monte Carlo algorithms such as control randomisation with policy iteration to avoid regression errors from accumulating. Presented numerical examples demonstrate that our transformation method allows for control of disturbance terms to be handled correctly and leads to an accurate solution. In addition, in the forward simulation stage of the algorithm, we propose a re-sampling of state variables at each time step instead of simulating continuous paths, to improve the exploration of the state space that also appears to be important to obtain a stable and accurate solution for expected utility models.
Download or read book Advanced Simulation Based Methods for Optimal Stopping and Control written by Denis Belomestny and published by Springer. This book was released on 2018-01-31 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.
Download or read book Monte Carlo Algorithms for Optimal Stopping and Statistical Learning Convergence Rates and Sample Complexity written by Daniel Egloff and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we extend the by now classical Longstaff-Schwartz algorithm for approximately solving high dimensional optimal stopping problems. We reformulate the problem of optimal stopping in discrete time as a generalized statistical learning problem. Within this setup we apply modern concentration inequalities for empirical means to study consistency criteria, convergence rates, and sample complexity estimates. Our results strengthen and extend earlier results obtained by Clement, Lamberton and Protter.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Simulation Based Methods for Optimal Stopping and Control written by Denis Belomestny and published by Palgrave Macmillan. This book was released on 2018-02-04 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.
Download or read book On non asymptotic optimal stopping criteria in Monte Carlo simulations written by Christian Bayer and published by . This book was released on 2013 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2010 written by Leszek Plaskota and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.
Download or read book Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Download or read book Optimal Learning written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2013-07-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting information is time-consuming and expensive. Designed for readers with an elementary background in probability and statistics, the book presents effective and practical policies illustrated in a wide range of applications, from energy, homeland security, and transportation to engineering, health, and business. This book covers the fundamental dimensions of a learning problem and presents a simple method for testing and comparing policies for learning. Special attention is given to the knowledge gradient policy and its use with a wide range of belief models, including lookup table and parametric and for online and offline problems. Three sections develop ideas with increasing levels of sophistication: Fundamentals explores fundamental topics, including adaptive learning, ranking and selection, the knowledge gradient, and bandit problems Extensions and Applications features coverage of linear belief models, subset selection models, scalar function optimization, optimal bidding, and stopping problems Advanced Topics explores complex methods including simulation optimization, active learning in mathematical programming, and optimal continuous measurements Each chapter identifies a specific learning problem, presents the related, practical algorithms for implementation, and concludes with numerous exercises. A related website features additional applications and downloadable software, including MATLAB and the Optimal Learning Calculator, a spreadsheet-based package that provides an introduction to learning and a variety of policies for learning.
Download or read book The Multi Dimensional Optimal Stopping Problem with Monte Carlo Simulation Results written by Minoru Yoshida and published by . This book was released on 1993 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Progress in Industrial Mathematics at ECMI 2006 written by Luis L. Bonilla and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings from the 14th European Conference for Mathematics in Industry held in Madrid present innovative numerical and mathematical techniques. Topics include the latest applications in aerospace, information and communications, materials, energy and environment, imaging, biology and biotechnology, life sciences, and finance. In addition, the conference also delved into education in industrial mathematics and web learning.
Download or read book Recent Advances in Financial Engineering written by Masaaki Kijima and published by World Scientific. This book was released on 2009 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2008 Daiwa International Workshop on Financial Engineering held in Tokyo. The annual workshop is sponsored by the Daiwa Securities Group, and serves as a bridge between leading academics and practitioners in the field. This year, the papers presented at the workshop have been refereed and published in a single volume to commemorate the 60th birthday of Professor Yuri Kabanov, and to thank him for his contributions to the progress of mathematical finance in general, and the Daiwa International Workshop in particular. This book caters to academics and practitioners as well as graduate and postgraduate students of financial engineering. Quantitative researchers on financial markets will also find it a useful resource.
Download or read book Mixing Monte Carlo and Partial Differential Equation Methods For Multi dimensional Optimal Stopping Problems Under Stochastic Volatility written by David Farahany and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we develop a numerical approach for solving multi-dimensional optimal stopping problems (OSPs) under stochastic volatility (SV) that combines least squares Monte Carlo (LSMC) with partial differential equation (PDE) techniques. The algorithm provides dimensional reduction from the PDE and regression perspective along with variance and dimensional reduction from the MC perspective. In Chapter 2, we begin by laying the mathematical foundation of mixed MC-PDE techniques for OSPs. Next, we show the basic mechanics of the algorithm and, under certain mild assumptions, prove it converges almost surely. We apply the algorithm to the one dimensional Heston model and demonstrate that the hybrid algorithm outperforms traditional LSMC techniques in terms of both estimating prices and optimal exercise boundaries (OEBs). In Chapter 3 we describe methods for reducing the complexity and run time of the algorithm along with techniques for computing sensitivities. To reduce the complexity, we apply two methods: clustering via sufficient statistics and multi-level Monte Carlo (mlMC)/multi-grids. While the clustering method allows us to reduce computational run times by a third for high dimensional problems, mlMC provides an order of magnitude reduction in complexity. To compute sensitivities, we employ a grid based method for derivatives with respect to the asset, S, and an MC method that uses initial dispersions for sensitivities with respect to variance, v. To test our approximations and computation of sensitivities, we revisit the one-dimensional Heston model and find our approximations introduce little-to-no error and that our computation of sensitivities is highly accurate in comparison to standard LSMC. To demonstrate the utility of our new computational techniques, we apply the hybrid algorithm to the multi-dimensional Heston model and show that the algorithm is highly accurate in terms of estimating prices, OEBs, and sensitivities, especially in comparison to standard LSMC. In Chapter 4 we highlight the importance of multi-factor SV models and apply our hybrid algorithm to two specific examples: the Double Heston model and a mean-reverting commodity model with jumps. Again, we were able to obtain low variance estimates of the prices, OEBs, and sensitivities.
Download or read book Optimization and Cooperative Control Strategies written by Michael Hirsch and published by Springer Science & Business Media. This book was released on 2009-01-17 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cooperative, collaborating autonomous systems are at the forefront of research efforts in numerous disciplines across the applied sciences. There is constant progress in solution techniques for these systems. However, despite this progress, cooperating systems have continued to be extremely difficult to model, analyze, and solve. Theoretical results are very difficult to come by. Each year, the International Conference on Cooperative Control and Optimization (CCO) brings together top researchers from around the world to present new, cutting-edge, ideas, theories, applications, and advances in the fields of autonomous agents, cooperative systems, control theory, information flow, and optimization. The works in this volume are a result of invited papers and selected presentations at the Eighth Annual International Conference on Cooperative Control and Optimization, held in Gainesville, Florida, January 30 – February 1, 2008.
Download or read book Recent Advances In Financial Engineering Proceedings Of The 2008 Daiwa International Workshop On Financial Engineering written by Masaaki Kijima and published by World Scientific. This book was released on 2009-06-02 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 2008 Daiwa International Workshop on Financial Engineering held in Tokyo. The annual workshop is sponsored by the Daiwa Securities Group, and serves as a bridge between leading academics and practitioners in the field. This year, the papers presented at the workshop have been refereed and published in a single volume to commemorate the 60th birthday of Professor Yuri Kabanov, and to thank him for his contributions to the progress of mathematical finance in general, and the Daiwa International Workshop in particular. The book caters to academics and practitioners as well as graduate and postgraduate students of financial engineering. Quantitative researchers on financial markets will also find it a useful resource.
Download or read book Stochastic Models Estimation and Control written by Peter S. Maybeck and published by Academic Press. This book was released on 1982-08-25 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
