Solving Free Boundary Problems With Applications In Finance
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Solving Free Boundary Problems With Applications In Finance
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Author : Kumar Muthuraman
language : en
Publisher: Now Publishers Inc
Release Date : 2008
Solving Free Boundary Problems With Applications In Finance written by Kumar Muthuraman and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Business & Economics categories.
Outlines and explains a recent computational method that solves free boundary problems by reducing them into a sequence of fixed boundary problems which are relatively easy to solve numerically.
Optimal Stopping And Free Boundary Problems
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Author : Goran Peskir
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-10
Optimal Stopping And Free Boundary Problems written by Goran Peskir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-10 with Mathematics categories.
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.
Free Boundary Problems
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Author : Isabel Narra Figueiredo
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-11
Free Boundary Problems written by Isabel Narra Figueiredo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-11 with Mathematics categories.
This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.
Numerical Methods In Scientific Computing
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Author : Jos van Kan
language : en
Publisher: TU Delft OPEN Publishing
Release Date : 2023-08-31
Numerical Methods In Scientific Computing written by Jos van Kan and has been published by TU Delft OPEN Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Mathematics categories.
This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of numerical solutions in the general modeling process and this must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account especially for validation of the numerical solution obtained. This book aims especially at engineers and scientists who have ’real world’ problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.
Free Boundary Problems In Pdes And Particle Systems
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Author : Gioia Carinci
language : en
Publisher: Springer
Release Date : 2016-06-22
Free Boundary Problems In Pdes And Particle Systems written by Gioia Carinci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-22 with Mathematics categories.
In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.
Functionals Of Multidimensional Diffusions With Applications To Finance
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Author : Jan Baldeaux
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Functionals Of Multidimensional Diffusions With Applications To Finance written by Jan Baldeaux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
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.
Fluctuations Of L Vy Processes With Applications
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Author : Andreas E. Kyprianou
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-09
Fluctuations Of L Vy Processes With Applications written by Andreas E. Kyprianou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Optimal Stopping Rules
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Author : Albert N. Shiryaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-23
Optimal Stopping Rules written by Albert N. Shiryaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-23 with Mathematics categories.
Although three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.
Antieigenvalue Analysis With Applications To Numerical Analysis Wavelets Statistics Quantum Mechanics Finance And Optimization
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Author : Karl Gustafson
language : en
Publisher: World Scientific
Release Date : 2011-12-23
Antieigenvalue Analysis With Applications To Numerical Analysis Wavelets Statistics Quantum Mechanics Finance And Optimization written by Karl Gustafson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
Karl Gustafson is the creator of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance.Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.
Continuous Time Stochastic Control And Optimization With Financial Applications
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Author : Huyên Pham
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-28
Continuous Time Stochastic Control And Optimization With Financial Applications written by Huyên Pham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-28 with Mathematics categories.
Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.