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Principles Of Optimal Stopping And Free Boundary Problems
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Book Synopsis Optimal Stopping and Free-Boundary Problems by : Goran Peskir
Download or read book Optimal Stopping and Free-Boundary Problems written by Goran Peskir and published by Springer Science & Business Media. This book was released on 2006-11-10 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Principles of Optimal Stopping and Free-boundary Problems by : Goran Peskir
Download or read book Principles of Optimal Stopping and Free-boundary Problems written by Goran Peskir and published by . This book was released on 2001 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE by : Nizar Touzi
Download or read book Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE written by Nizar Touzi and published by Springer Science & Business Media. This book was released on 2012-09-25 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Book Synopsis Regularity of Free Boundaries in Obstacle-Type Problems by : Arshak Petrosyan
Download or read book Regularity of Free Boundaries in Obstacle-Type Problems written by Arshak Petrosyan and published by American Mathematical Soc.. This book was released on 2012 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
Author :Isabel Narra Figueiredo Publisher :Springer Science & Business Media ISBN 13 :3764377194 Total Pages :461 pages Book Rating :4.7/5 (643 download)
Book Synopsis Free Boundary Problems by : Isabel Narra Figueiredo
Download or read book Free Boundary Problems written by Isabel Narra Figueiredo and published by Springer Science & Business Media. This book was released on 2007-01-11 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The obstacle problem by : Luis Angel Caffarelli
Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Book Synopsis Free Boundary Problems Involving Solids by : J M Chadam
Download or read book Free Boundary Problems Involving Solids written by J M Chadam and published by CRC Press. This book was released on 1993-02-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.
Book Synopsis Free Boundary Problems by : J I Diaz
Download or read book Free Boundary Problems written by J I Diaz and published by CRC Press. This book was released on 1995-04-04 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research note consists of selected contributions from the 1993 International Conference on "Free Boundary Problems: Theory and Applications." These represent coherent and high-level research in the field of free boundary problems. Topics include mean curvature flows, phase transitions and material sciences, fluid mechanics and combustion problems.
Book Synopsis Recent Advances in Applied Probability by : Ricardo Baeza-Yates
Download or read book Recent Advances in Applied Probability written by Ricardo Baeza-Yates and published by Springer Science & Business Media. This book was released on 2006-02-28 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.
Book Synopsis The Theory of Optimal Stopping by : Yuan Shih Chow
Download or read book The Theory of Optimal Stopping written by Yuan Shih Chow and published by Dover Publications. This book was released on 1991-01 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Free Boundary Problems in Fluid Flow with Applications by : J M Chadam
Download or read book Free Boundary Problems in Fluid Flow with Applications written by J M Chadam and published by CRC Press. This book was released on 1993-02-22 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third of three volumes containing the proceedings of the International Colloquium 'Free Boundary problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main part of this volume studies the flow of fluids, an area which has led to many of the classical free boundary problems. The first two sections contain the papers on various problems in fluid mechanics. The types of problems vary fromthe collision of two jets to the growth of a sand wave. In the next two sections porous flow is considered. This has important practical applications in fields such as petroleum engineering and groundwater pollution. Some new and interesting free boundary problems in geology and engineering are treated in the final section.
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Book Synopsis Advances in Finance and Stochastics by : Klaus Sandmann
Download or read book Advances in Finance and Stochastics written by Klaus Sandmann and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.
Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham
Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control of Nonsmooth Distributed Parameter Systems by : Dan Tiba
Download or read book Optimal Control of Nonsmooth Distributed Parameter Systems written by Dan Tiba and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
Book Synopsis Some Mathematical Questions in Biology by : Simon A. Levin
Download or read book Some Mathematical Questions in Biology written by Simon A. Levin and published by American Mathematical Soc.. This book was released on 1979-12-31 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with problems in epidemiology, allergic reactions, resource management, and presents a model of respiration
Book Synopsis Lecture Notes Series by : Aarhus universitet. Matematisk institut
Download or read book Lecture Notes Series written by Aarhus universitet. Matematisk institut and published by . This book was released on 2001 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
