Lectures On Bsdes Stochastic Control And Stochastic Differential Games With Financial Applications

Author : Rene Carmona
Publisher : SIAM
Page : 265 pages
File Size : 51,7 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974249

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Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Author : Rene Carmona
Publisher : SIAM
Page : 263 pages
File Size : 52,6 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974232

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Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Author : Jianfeng Zhang
Publisher : Springer
Page : 388 pages
File Size : 54,5 Mb
Release : 2017-08-22
Category : Mathematics
ISBN : 9781493972562

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Backward Stochastic Differential Equations by Jianfeng Zhang Pdf

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.

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 47,9 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

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Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Author : Selim S. Hacısalihzade
Publisher : Springer
Page : 303 pages
File Size : 42,6 Mb
Release : 2017-12-28
Category : Mathematics
ISBN : 9783319644929

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Control Engineering and Finance by Selim S. Hacısalihzade Pdf

This book includes a review of mathematical tools like modelling, analysis of stochastic processes, calculus of variations and stochastic differential equations which are applied to solve financial problems like modern portfolio theory and option pricing. Every chapter presents exercises which help the reader to deepen his understanding. The target audience comprises research experts in the field of finance engineering, but the book may also be beneficial for graduate students alike.

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 138 pages
File Size : 47,6 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030483067

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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Author : George Yin,Thaleia Zariphopoulou
Publisher : Springer Nature
Page : 466 pages
File Size : 46,5 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9783030985196

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Stochastic Analysis, Filtering, and Stochastic Optimization by George Yin,Thaleia Zariphopoulou Pdf

This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.

Author : Christian Bayer,Peter K. Friz,Masaaki Fukasawa,Jim Gatheral,Antoine Jacquier,Mathieu Rosenbaum
Publisher : SIAM
Page : 292 pages
File Size : 51,7 Mb
Release : 2023-12-18
Category : Mathematics
ISBN : 9781611977783

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Rough Volatility by Christian Bayer,Peter K. Friz,Masaaki Fukasawa,Jim Gatheral,Antoine Jacquier,Mathieu Rosenbaum Pdf

Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves essentially as a fractional Brownian motion with a small Hurst parameter. The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression. This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.

Author : Rainer Buckdahn,Hans J. Engelbert,Marc Yor
Publisher : CRC Press
Page : 296 pages
File Size : 53,9 Mb
Release : 2002-05-16
Category : Mathematics
ISBN : 9781482265231

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Stochastic Processes and Related Topics by Rainer Buckdahn,Hans J. Engelbert,Marc Yor Pdf

This volume comprises selected papers presented at the 12th Winter School on Stochastic Processes and their Applications, which was held in Siegmundsburg, Germany, in March 2000. The contents include Backward Stochastic Differential Equations; Semilinear PDE and SPDE; Arbitrage Theory; Credit Derivatives and Models for Correlated Defaults; Three In

Author : M. H. A. Davis
Publisher : Springer
Page : 130 pages
File Size : 48,7 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015015718136

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Lectures on Stochastic Control and Nonlinear Filtering by M. H. A. Davis Pdf

Author : N El Karoui,Laurent Mazliak
Publisher : CRC Press
Page : 236 pages
File Size : 47,7 Mb
Release : 1997-01-17
Category : Mathematics
ISBN : 0582307333

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Backward Stochastic Differential Equations by N El Karoui,Laurent Mazliak Pdf

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.

Author : Andrzej S. Nowak,Krzysztof Szajowski
Publisher : Birkhäuser
Page : 679 pages
File Size : 54,9 Mb
Release : 2008-11-01
Category : Business & Economics
ISBN : 0817670807

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Advances in Dynamic Games by Andrzej S. Nowak,Krzysztof Szajowski Pdf

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a guide to the vitality and growth of the field. A valuable reference for researchers and practitioners in dynamic game theory, it covers a broad range of topics and applications, including repeated and stochastic games, differential dynamic games, optimal stopping games, and numerical methods and algorithms for solving dynamic games. The diverse topics included will also benefit researchers and graduate students in applied mathematics, economics, engineering, systems and control, and environmental science.

Author : Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski
Publisher : SIAM
Page : 512 pages
File Size : 45,5 Mb
Release : 2014-07-09
Category : Mathematics
ISBN : 9781611973433

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Lectures on Stochastic Programming by Alexander Shapiro,Darinka Dentcheva,Andrzej Ruszczy?ski Pdf

Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 46,7 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

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Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

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.

Author : Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas
Publisher : Springer
Page : 734 pages
File Size : 42,6 Mb
Release : 2019-01-13
Category : Mathematics
ISBN : 9783030015930

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Computation and Combinatorics in Dynamics, Stochastics and Control by Elena Celledoni,Giulia Di Nunno,Kurusch Ebrahimi-Fard,Hans Zanna Munthe-Kaas Pdf

The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.