Robust Utility Maximization With Nonlinear Continuous Semimartingales

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Continuous-time Stochastic Control and Optimization with Financial Applications

Author : Huyên Pham
Publisher : Springer Science & Business Media
ISBN 13 : 3540895000
Total Pages : 243 pages
Book Rating : 4.5/5 (48 download)

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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.

Backward Stochastic Differential Equations

Author : Jianfeng Zhang
Publisher : Springer
ISBN 13 : 1493972561
Total Pages : 392 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Backward Stochastic Differential Equations by : Jianfeng Zhang

Download or read book Backward Stochastic Differential Equations written by Jianfeng Zhang and published by Springer. This book was released on 2017-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Continuous-Time Finance

Author : Robert C. Merton
Publisher : Wiley-Blackwell
ISBN 13 : 9780631185086
Total Pages : 754 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Continuous-Time Finance by : Robert C. Merton

Download or read book Continuous-Time Finance written by Robert C. Merton and published by Wiley-Blackwell. This book was released on 1992-11-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.

Backward Stochastic Differential Equations

Author : N El Karoui
Publisher : CRC Press
ISBN 13 : 9780582307339
Total Pages : 236 pages
Book Rating : 4.3/5 (73 download)

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Book Synopsis Backward Stochastic Differential Equations by : N El Karoui

Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Applied Intertemporal Optimization

Author : Klaus Wälde
Publisher : Klaus Wälde
ISBN 13 : 3000324283
Total Pages : 332 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Applied Intertemporal Optimization by : Klaus Wälde

Download or read book Applied Intertemporal Optimization written by Klaus Wälde and published by Klaus Wälde. This book was released on 2012 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1804 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1804 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Financial Modelling with Jump Processes

Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Financial Modelling with Jump Processes by : Peter Tankov

Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Conjugate Duality and Optimization

Author : R. Tyrrell Rockafellar
Publisher : SIAM
ISBN 13 : 9781611970524
Total Pages : 80 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Conjugate Duality and Optimization by : R. Tyrrell Rockafellar

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Arbitrage Theory in Continuous Time

Author : Tomas Björk
Publisher : OUP Oxford
ISBN 13 : 0191610291
Total Pages : 600 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Björk

Download or read book Arbitrage Theory in Continuous Time written by Tomas Björk and published by OUP Oxford. This book was released on 2009-08-06 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Mathematical Finance

Author : Ernst Eberlein
Publisher : Springer Nature
ISBN 13 : 3030261069
Total Pages : 774 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Mathematical Finance by : Ernst Eberlein

Download or read book Mathematical Finance written by Ernst Eberlein and published by Springer Nature. This book was released on 2019-12-03 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Probability Theory and Stochastic Processes with Applications (Second Edition)

Author : Oliver Knill
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813109490
Total Pages : 500 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Probability Theory and Stochastic Processes with Applications (Second Edition) by : Oliver Knill

Download or read book Probability Theory and Stochastic Processes with Applications (Second Edition) written by Oliver Knill and published by World Scientific Publishing Company. This book was released on 2017-01-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

Enlargement of Filtration with Finance in View

Author : Anna Aksamit
Publisher : Springer
ISBN 13 : 3319412558
Total Pages : 155 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Enlargement of Filtration with Finance in View by : Anna Aksamit

Download or read book Enlargement of Filtration with Finance in View written by Anna Aksamit and published by Springer. This book was released on 2017-11-18 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents classical results of the theory of enlargement of filtration. The focus is on the behavior of martingales with respect to the enlarged filtration and related objects. The study is conducted in various contexts including immersion, progressive enlargement with a random time and initial enlargement with a random variable. The aim of this book is to collect the main mathematical results (with proofs) previously spread among numerous papers, great part of which is only available in French. Many examples and applications to finance, in particular to credit risk modelling and the study of asymmetric information, are provided to illustrate the theory. A detailed summary of further connections and applications is given in bibliographic notes which enables to deepen study of the topic. This book fills a gap in the literature and serves as a guide for graduate students and researchers interested in the role of information in financial mathematics and in econometric science. A basic knowledge of the general theory of stochastic processes is assumed as a prerequisite.

Financial Markets Theory

Author : Emilio Barucci
Publisher : Springer
ISBN 13 : 1447173228
Total Pages : 843 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Financial Markets Theory by : Emilio Barucci

Download or read book Financial Markets Theory written by Emilio Barucci and published by Springer. This book was released on 2017-06-08 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises. Financial Markets Theory covers classical asset pricing theory in great detail, including utility theory, equilibrium theory, portfolio selection, mean-variance portfolio theory, CAPM, CCAPM, APT, and the Modigliani-Miller theorem. Starting from an analysis of the empirical evidence on the theory, the authors provide a discussion of the relevant literature, pointing out the main advances in classical asset pricing theory and the new approaches designed to address asset pricing puzzles and open problems (e.g., behavioral finance). Later chapters in the book contain more advanced material, including on the role of information in financial markets, non-classical preferences, noise traders and market microstructure. This textbook is aimed at graduate students in mathematical finance and financial economics, but also serves as a useful reference for practitioners working in insurance, banking, investment funds and financial consultancy. Introducing necessary tools from microeconomic theory, this book is highly accessible and completely self-contained. Advance praise for the second edition: "Financial Markets Theory is comprehensive, rigorous, and yet highly accessible. With their second edition, Barucci and Fontana have set an even higher standard!"Darrell Duffie, Dean Witter Distinguished Professor of Finance, Graduate School of Business, Stanford University "This comprehensive book is a great self-contained source for studying most major theoretical aspects of financial economics. What makes the book particularly useful is that it provides a lot of intuition, detailed discussions of empirical implications, a very thorough survey of the related literature, and many completely solved exercises. The second edition covers more ground and provides many more proofs, and it will be a handy addition to the library of every student or researcher in the field."Jaksa Cvitanic, Richard N. Merkin Professor of Mathematical Finance, Caltech "The second edition of Financial Markets Theory by Barucci and Fontana is a superb achievement that knits together all aspects of modern finance theory, including financial markets microstructure, in a consistent and self-contained framework. Many exercises, together with their detailed solutions, make this book indispensable for serious students in finance."Michel Crouhy, Head of Research and Development, NATIXIS

Continuous Exponential Martingales and BMO

Author : Norihiko Kazamaki
Publisher : Springer
ISBN 13 : 3540484213
Total Pages : 102 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Continuous Exponential Martingales and BMO by : Norihiko Kazamaki

Download or read book Continuous Exponential Martingales and BMO written by Norihiko Kazamaki and published by Springer. This book was released on 2006-11-15 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Author : Nizar Touzi
Publisher : Springer Science & Business Media
ISBN 13 : 1461442869
Total Pages : 219 pages
Book Rating : 4.4/5 (614 download)

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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.

Indifference Pricing

Author : René Carmona
Publisher : Princeton University Press
ISBN 13 : 0691138834
Total Pages : 427 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Indifference Pricing by : René Carmona

Download or read book Indifference Pricing written by René Carmona and published by Princeton University Press. This book was released on 2009-01-18 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. René Carmona brings together a who's who of leading experts in the field to provide the definitive introduction for students, scholars, and researchers. Until recently, financial mathematicians and engineers developed pricing and hedging procedures that assumed complete markets. But markets are generally incomplete, and it may be impossible to hedge against all sources of randomness. Indifference Pricing offers cutting-edge procedures developed under more realistic market assumptions. The book begins by introducing the concept of indifference pricing in the simplest possible models of discrete time and finite state spaces where duality theory can be exploited readily. It moves into a more technical discussion of utility indifference pricing for diffusion models, and then addresses problems of optimal design of derivatives by extending the indifference pricing paradigm beyond the realm of utility functions into the realm of dynamic risk measures. Focus then turns to the applications, including portfolio optimization, the pricing of defaultable securities, and weather and commodity derivatives. The book features original mathematical results and an extensive bibliography and indexes. In addition to the editor, the contributors are Pauline Barrieu, Tomasz R. Bielecki, Nicole El Karoui, Robert J. Elliott, Said Hamadène, Vicky Henderson, David Hobson, Aytac Ilhan, Monique Jeanblanc, Mattias Jonsson, Anis Matoussi, Marek Musiela, Ronnie Sircar, John van der Hoek, and Thaleia Zariphopoulou. The first book on utility indifference pricing Explains the fundamentals of indifference pricing, from simple models to the most technical ones Goes beyond utility functions to analyze optimal risk transfer and the theory of dynamic risk measures Covers non-Markovian and partially observed models and applications to portfolio optimization, defaultable securities, static and quadratic hedging, weather derivatives, and commodities Includes extensive bibliography and indexes Provides essential reading for PhD students, researchers, and professionals