Nonlinear Expectations And Stochastic Calculus Under Uncertainty
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Nonlinear Expectations And Stochastic Calculus Under Uncertainty
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Author : Shige Peng
language : en
Publisher:
Release Date : 2019
Nonlinear Expectations And Stochastic Calculus Under Uncertainty written by Shige Peng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Distribution (Probability theory) categories.
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
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Author : Shige Peng
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
Nonlinear Expectations And Stochastic Calculus Under Uncertainty written by Shige Peng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
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.
Real Options Ambiguity Risk And Insurance
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Author : A. Bensoussan
language : en
Publisher: IOS Press
Release Date : 2013-05-02
Real Options Ambiguity Risk And Insurance written by A. Bensoussan and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Business & Economics categories.
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.
Stochastic Pdes And Modelling Of Multiscale Complex System
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Author : Xiaopeng Chen
language : en
Publisher: World Scientific
Release Date : 2019-05-07
Stochastic Pdes And Modelling Of Multiscale Complex System written by Xiaopeng Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
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.
Recent Advances In Financial Engineering 2014
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Author : Masaaki Kijima
language : en
Publisher: World Scientific
Release Date : 2016
Recent Advances In Financial Engineering 2014 written by Masaaki Kijima and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electronic books categories.
"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
Recent Advances In Financial Engineering 2014 Proceedings Of The Tmu Finance Workshop 2014
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Author : Masaaki Kijima
language : en
Publisher: World Scientific
Release Date : 2016-02-29
Recent Advances In Financial Engineering 2014 Proceedings Of The Tmu Finance Workshop 2014 written by Masaaki Kijima and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-29 with Business & Economics categories.
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.
Stochastic Numerics For Mathematical Physics
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Author : Grigori N. Milstein
language : en
Publisher: Springer Nature
Release Date : 2021-12-03
Stochastic Numerics For Mathematical Physics written by Grigori N. Milstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-03 with Computers categories.
This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Mathematical Control Theory For Stochastic Partial Differential Equations
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Author : Qi Lü
language : en
Publisher: Springer Nature
Release Date : 2021-09-17
Mathematical Control Theory For Stochastic Partial Differential Equations written by Qi Lü and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-17 with Science categories.
This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Combining Modelling And Analyzing Imprecision Randomness And Dependence
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Author : Jonathan Ansari
language : en
Publisher: Springer Nature
Release Date : 2024-08-09
Combining Modelling And Analyzing Imprecision Randomness And Dependence written by Jonathan Ansari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-09 with Computers categories.
This volume contains more than 65 peer-reviewed papers corresponding to presentations at the 11th Conference on Soft Methods in Probability and Statistics (SMPS) held in Salzburg, Austria, in September 2024. It covers recent advances in the field of probability, statistics, and data science, with a particular focus on dealing with dependence, imprecision and incomplete information. Reflecting the fact that data science continues to evolve, this book serves as a bridge between different groups of experts, including statisticians, mathematicians, computer scientists, and engineers, and encourages interdisciplinary research. The selected contributions cover a wide range of topics such as imprecise probabilities, random sets, belief functions, possibility theory, and dependence modeling. Readers will find discussions on clustering, depth concepts, dimensionality reduction, and robustness, reflecting the conference's commitment to addressing real-world challenges through innovative methods.