Search results for: optimal-stopping-and-free-boundary-problems

Optimal Stopping and Free Boundary Problems

Author : Goran Peskir
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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.

Principles of Optimal Stopping and Free boundary Problems

Author : Goran Peskir
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Optimal Stopping and Free Boundary Problems

Author : Goran Peskir
File Size : 35.75 MB
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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.

Solving Free boundary Problems with Applications in Finance

Author : Kumar Muthuraman
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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.

Free Boundary Problems

Author : Isabel Narra Figueiredo
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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.

Free Boundary Problems in PDEs and Particle Systems

Author : Gioia Carinci
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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.

Boundary Value Problems for Linear Evolution Partial Differential Equations

Author : H.G. Garnir
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Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,,

Continuous time Stochastic Control and Optimization with Financial Applications

Author : Huyên Pham
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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.

Variational Principles and Free boundary Problems

Author : Avner Friedman
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This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters -- covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form -- are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.

Finance at Fields

Author : Matheus R. Grasselli
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This outstanding collection of articles includes papers presented at the Fields Institute, Toronto, as part of the Thematic Program in Quantitative Finance that took place in the first six months of the year 2010. The scope of the volume in very broad, including papers on foundational issues in mathematical finance, papers on computational finance, and papers on derivatives and risk management. Many of the papers contain path-breaking insights that are relevant to the developing new order of post-crisis financial risk management.

Free Boundary Problems

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Modern Software Tools for Scientific Computing

Author : E. Arge
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The purpose of this book is to survey some recent advances in the development of software tools for scientific computing. This book presents 17 carefully selected and refereed chapters originally presented at the SciTools '96 Workshop in Oslo, Norway. The chapters emphasize the design of large software codes, computational efficiency, object-oriented programming in scientific computing, reliability of numerical software, and parallel computing.

Mathematical Control Theory and Finance

Author : Andrey Sarychev
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Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.

Free Boundary Problems

Author : Antonio Fasano
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Mathematical Methods for Financial Markets

Author : Monique Jeanblanc
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Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

Exotic Option Pricing and Advanced L vy Models

Author : Andreas Kyprianou
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Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

Mathematical Finance Theory Review and Exercises

Author : Emanuela Rosazza Gianin
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The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

Boundary Value Problems for Linear Evolution Partial Differential Equations

Author : Henri G. Garnir
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Recursive Integration and Optimal Stopping

Author : Tiong Wee Lim
File Size : 82.36 MB
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Proceedings of A Razmadze Mathematical Institute

Author :
File Size : 31.38 MB
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