Download or read book RKHS Regularization of Singular Local Stochastic Volatility McKean Vlasov Models written by Christian Bayer and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the challenges related to the calibration of financial models, we consider the problem of solving numerically a singular McKean-Vlasov equation, which represents a singular local stochastic volatility model. Whilst such models are quite popular among practitioners, unfortunately, its well-posedness has not been fully understood yet and, in general, is possibly not guaranteed at all. We develop a novel regularization approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularized model is well-posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularized model is able to perfectly replicate option prices due to typical local volatility models. Our results are also applicable to more general McKean-Vlasov equations.
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Aicke Hinrichs and published by Springer Nature. This book was released on with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastics in Finite and Infinite Dimensions written by Takeyuki Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.
Download or read book Paris Princeton Lectures on Mathematical Finance 2013 written by Fred Espen Benth and published by Springer. This book was released on 2013-07-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current volume presents four chapters touching on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy markets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Manolarakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.
Download or read book Probabilistic Theory of Mean Field Games with Applications I written by René Carmona and published by Springer. This book was released on 2018-03-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Download or read book Advanced Modelling in Mathematical Finance written by Jan Kallsen and published by Springer. This book was released on 2016-12-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.
Download or read book Support Vector Machines written by Ingo Steinwart and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical. David Hilbert The goal of this book is to explain the principles that made support vector machines (SVMs) a successful modeling and prediction tool for a variety of applications. We try to achieve this by presenting the basic ideas of SVMs together with the latest developments and current research questions in a uni?ed style. In a nutshell, we identify at least three reasons for the success of SVMs: their ability to learn well with only a very small number of free parameters, their robustness against several types of model violations and outliers, and last but not least their computational e?ciency compared with several other methods. Although there are several roots and precursors of SVMs, these methods gained particular momentum during the last 15 years since Vapnik (1995, 1998) published his well-known textbooks on statistical learning theory with aspecialemphasisonsupportvectormachines. Sincethen,the?eldofmachine learninghaswitnessedintenseactivityinthestudyofSVMs,whichhasspread moreandmoretootherdisciplinessuchasstatisticsandmathematics. Thusit seems fair to say that several communities are currently working on support vector machines and on related kernel-based methods. Although there are many interactions between these communities, we think that there is still roomforadditionalfruitfulinteractionandwouldbegladifthistextbookwere found helpful in stimulating further research. Many of the results presented in this book have previously been scattered in the journal literature or are still under review. As a consequence, these results have been accessible only to a relativelysmallnumberofspecialists,sometimesprobablyonlytopeoplefrom one community but not the others.
Download or read book The Volatility Surface written by Jim Gatheral and published by . This book was released on 2006 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variable Structure Systems written by Asif Sabanovic and published by IET. This book was released on 2004-10-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book fulfils the definite need for an accessible book on variable structure systems and also provides the very latest results in research on this topic. Divided into three parts - basics of sliding mode control, new trends in sliding mode control, and applications of sliding mode control - the book contains many numerical design examples, so that readers can quickly understand the design methodologies and their applications to practical problems. Primarily aimed at students and researchers in the field, the book will also be useful for practising control engineers.
Download or read book Object Oriented Data Analysis written by J. S. Marron and published by CRC Press. This book was released on 2021-11-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.
Download or read book Cure Models written by Yingwei Peng and published by CRC Press. This book was released on 2021-03-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cure Models: Methods, Applications and Implementation is the first book in the last 25 years that provides a comprehensive and systematic introduction to the basics of modern cure models, including estimation, inference, and software. This book is useful for statistical researchers and graduate students, and practitioners in other disciplines to have a thorough review of modern cure model methodology and to seek appropriate cure models in applications. The prerequisites of this book include some basic knowledge of statistical modeling, survival models, and R and SAS for data analysis. The book features real-world examples from clinical trials and population-based studies and a detailed introduction to R packages, SAS macros, and WinBUGS programs to fit some cure models. The main topics covered include the foundation of statistical estimation and inference of cure models for independent and right-censored survival data, cure modeling for multivariate, recurrent-event, and competing-risks survival data, and joint modeling with longitudinal data, statistical testing for the existence and difference of cure rates and sufficient follow-up, new developments in Bayesian cure models, applications of cure models in public health research and clinical trials.
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Download or read book Lectures on the Coupling Method written by Torgny Lindvall and published by Courier Corporation. This book was released on 2012-08-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
Download or read book Adiabatic Perturbation Theory in Quantum Dynamics written by Stefan Teufel and published by Springer Science & Business Media. This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stein s Method and Applications written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 1983, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.
Download or read book Encyclopedia of Applied and Computational Mathematics written by Björn Engquist and published by Springer. This book was released on 2016-12-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.
