Affine Diffusions and Related Processes Simulation Theory and Applications

Author: Aurélien Alfonsi
Publisher: Springer
ISBN: 3319052217
Format: PDF, ePub
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This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.

Numerical Probability

Author: Gilles Pagès
Publisher: Springer
ISBN: 3319902768
Format: PDF, Mobi
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This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance. Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.

Functionals of Multidimensional Diffusions with Applications to Finance

Author: Jan Baldeaux
Publisher: Springer Science & Business Media
ISBN: 3319007475
Format: PDF, ePub, Mobi
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This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Parameter Estimation in Fractional Diffusion Models

Author: Kęstutis Kubilius
Publisher: Springer
ISBN: 3319710303
Format: PDF, ePub, Docs
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This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Peacocks and Associated Martingales with Explicit Constructions

Author: Francis Hirsch
Publisher: Springer Science & Business Media
ISBN: 8847019087
Format: PDF, Kindle
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We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are developed in eight chapters, with about a hundred of exercises.

Advances in Theoretical and Applied Statistics

Author: Nicola Torelli
Publisher: Springer Science & Business Media
ISBN: 3642355889
Format: PDF, Mobi
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This volume includes contributions selected after a double blind review process and presented as a preliminary version at the 45th Meeting of the Italian Statistical Society. The papers provide significant and innovative original contributions and cover a broad range of topics including: statistical theory; methods for time series and spatial data; statistical modeling and data analysis; survey methodology and official statistics; analysis of social, demographic and health data; and economic statistics and econometrics.

Advances in Multimedia Modeling

Author: Klaus Schoeffmann
Publisher: Springer
ISBN: 3642273556
Format: PDF, ePub, Mobi
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This book constitutes the refereed proceedings of the 18th International Multimedia Modeling Conference, MMM 2012, held in Klagenfurt, Austria, in January 2012. The 38 revised regular papers, 12 special session papers, 15 poster session papers, and 6 demo session papers were carefully reviewed and selected from 142 submissions. The papers are organized in the following topical sections: annotation, annotation and interactive multimedia applications, event and activity, mining and mobile multimedia applications, search, summarization and visualization, visualization and advanced multimedia systems, and the special sessions: interactive and immersive entertainment and communication, multimedia preservation: how to ensure multimedia access over time, multi-modal and cross-modal search, and video surveillance.

Proceedings of the 2010 Academy of Marketing Science AMS Annual Conference

Author: Dawn R. Deeter-Schmelz
Publisher: Springer
ISBN: 3319117971
Format: PDF, ePub
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Founded in 1971, the Academy of Marketing Science is an international organization dedicated to promoting timely explorations of phenomena related to the science of marketing in theory, research, and practice. Among its services to members and the community at large, the Academy offers conferences, congresses and symposia that attract delegates from around the world. Presentations from these events are published in this Proceedings series, which offers a comprehensive archive of volumes reflecting the evolution of the field. Volumes deliver cutting-edge research and insights, complimenting the Academy’s flagship journals, the Journal of the Academy of Marketing Science (JAMS) and AMS Review. Volumes are edited by leading scholars and practitioners across a wide range of subject areas in marketing science. This volume includes the full proceedings from the 2010 Academy of Marketing Science (AMS) Annual Conference held in Portland, Oregon.

Large Deviations and Asymptotic Methods in Finance

Author: Peter K. Friz
Publisher: Springer
ISBN: 3319116053
Format: PDF, Mobi
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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.

Diffusions Markov Processes and Martingales Volume 1 Foundations

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 1107717493
Format: PDF, ePub, Docs
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Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.