Nonlinear Expectations and Stochastic Calculus under Uncertainty
Nonlinear Expectations and Stochastic Calculus under Uncertainty

Author: Shige Peng

Publisher: Springer Nature

Published: 2019-09-09

Total Pages: 216

ISBN-13: 3662599031

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This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.

Nonlinear Expectations and Stochastic Calculus Under Uncertainty
Nonlinear Expectations and Stochastic Calculus Under Uncertainty

Author: Shige Peng

Publisher:

Published: 2019

Total Pages: 212

ISBN-13: 9783662599044

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This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng's lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.

Nonlinear Valuation and Non-Gaussian Risks in Finance
Nonlinear Valuation and Non-Gaussian Risks in Finance

Author: Dilip B. Madan

Publisher: Cambridge University Press

Published: 2022-02-03

Total Pages: 284

ISBN-13: 100900249X

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What happens to risk as the economic horizon goes to zero and risk is seen as an exposure to a change in state that may occur instantaneously at any time? All activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically at a zero time horizon, with arrival rates at the core of the modeling. This book, aimed at practitioners and researchers in financial risk, delivers the theoretical framework and various applications of the newly established dynamic conic finance theory. The result is a nonlinear non-Gaussian valuation framework for risk management in finance. Risk-free assets disappear and low risk portfolios must pay for their risk reduction with negative expected returns. Hedges may be constructed to enhance value by exploiting risk interactions. Dynamic trading mechanisms are synthesized by machine learning algorithms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.

Real Options, Ambiguity, Risk and Insurance
Real Options, Ambiguity, Risk and Insurance

Author: A. Bensoussan

Publisher: IOS Press

Published: 2013-05-02

Total Pages: 296

ISBN-13: 161499238X

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Financial engineering has become the focus of widespread media attention as a result of the worldwide financial crisis of recent years. This book is the second in a series dealing with financial engineering from Ajou University in Korea. The main objective of the series is to disseminate recent developments and important issues in financial engineering to graduate students and researchers, and to provide surveys or pedagogical exposition of important published papers in a broad perspective, as well as analyses of important financial news concerning financial engineering research, practices or regulations. Real Options, Ambiguity, Risk and Insurance, comprises 12 chapters and is divided into three parts. In Part I, five chapters deal with real options analysis, which addresses the issue of investment decisions in complex, innovative or risky projects. Part II presents three chapters on ambiguity. The notion of ambiguity is one of the major breakthroughs in the expected utility theory; ambiguity arises as uncertainties cannot be precisely described in the probability space. Part III consists of four chapters devoted to risk and insurance, and covers mutual insurance for non-traded risks, downside risk management, and credit risk in fixed income markets. This volume will be useful to both graduate students and researchers in understanding relatively new areas in economics and finance, as well as challenging aspects of mathematics.

Backward Stochastic Differential Equations
Backward Stochastic Differential Equations

Author: N El Karoui

Publisher: CRC Press

Published: 1997-01-17

Total Pages: 236

ISBN-13: 9780582307339

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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.

Stochastic Pdes And Modelling Of Multiscale Complex System
Stochastic Pdes And Modelling Of Multiscale Complex System

Author: Xiaopeng Chen

Publisher: World Scientific

Published: 2019-05-07

Total Pages: 238

ISBN-13: 981120036X

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This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

Applied Stochastic Differential Equations
Applied Stochastic Differential Equations

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2019-05-02

Total Pages: 327

ISBN-13: 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Elementary Stochastic Calculus with Finance in View
Elementary Stochastic Calculus with Finance in View

Author: Thomas Mikosch

Publisher: World Scientific

Published: 1998

Total Pages: 230

ISBN-13: 9789810235437

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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Recent Advances in Financial Engineering 2014
Recent Advances in Financial Engineering 2014

Author: Masaaki Kijima

Publisher: World Scientific

Published: 2016

Total Pages: 237

ISBN-13: 9814730777

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"Since 2004, the Tokyo Metropolitan University (TMU) has been conducting workshops that serve as a forum for academic researchers and practitioners to exchange ideas and developments in different fields of finance. This book is based on papers presented at the 2014 workshop held in Tokyo, on 6-7 November, 2014. The chapters address state-of-the-art techniques in mathematical finance and financial engineering. The authors share ideas and information on new methods and up-to-date results of their research in these fields. This book is a must-read for researchers, practitioners, and graduate students in the fields of mathematical finance, quantitative finance and financial engineering."--Provided by publisher