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Lectures on Financial Mathematics

Author: Greg Anderson

Publisher: Springer Nature

Published: 2022-06-01

Total Pages: 51

ISBN-13: 3031023994

This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets

Paris-Princeton Lectures on Mathematical Finance 2002

Author: Peter Bank

Publisher: Springer

Published: 2003-12-15

Total Pages: 178

ISBN-13: 3540448594

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The Paris-Princeton Lectures in Financial Mathematics, of which this is the first volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming! - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with articles by P. Bank/H. Föllmer, F. Baudoin, L.C.G. Rogers, and M. Soner/N. Touzi.

Lectures on the Mathematics of Finance

Author: Ioannis Karatzas

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 163

ISBN-13: 0821809091

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In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.

Mathematics of Finance

Author: Donald G. Saari

Publisher: Springer Nature

Published: 2019-08-31

Total Pages: 144

ISBN-13: 3030254437

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This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.

Lectures On Mathematical Finance And Related Topics

Author: Yuri Kifer

Publisher: World Scientific

Published: 2019-12-19

Total Pages: 345

ISBN-13: 9811209588

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Rigorous mathematical finance relies strongly on two additional fields: optimal stopping and stochastic analysis. This book is the first one which presents not only main results in the mathematical finance but also these 'related topics' with all proofs and in a self-contained form. The book treats both discrete and continuous time mathematical finance. Some topics, such as Israeli (game) contingent claims, and several proofs have not appeared before in a self-contained book form. The book contains exercises with solutions at the end of it and it can be used for a yearlong advanced graduate course for mathematical students.

Paris-Princeton Lectures on Mathematical Finance 2010

Author: Areski Cousin

Publisher: Springer Science & Business Media

Published: 2011-06-29

Total Pages: 374

ISBN-13: 3642146597

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The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

Lectures on Financial Mathematics

Author: Greg Anderson

Publisher: Morgan & Claypool Publishers

Published: 2010

Total Pages: 51

ISBN-13: 1608454959

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This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage," the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets

Paris-Princeton Lectures on Mathematical Finance 2004

Author: René Carmona

Publisher: Springer

Published: 2007-08-10

Total Pages: 248

ISBN-13: 3540733272

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This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by René Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyên Pham.

Paris-Princeton Lectures on Mathematical Finance 2003

Author: Tomasz R. Bielecki

Publisher: Springer

Published: 2004-08-30

Total Pages: 254

ISBN-13: 3540444688

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The Paris-Princeton Lectures in Financial Mathematics, of which this is the second volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming! - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. This volume presents the following articles: "Hedging of Defaultable Claims" by T. Bielecki, M. Jeanblanc, and M. Rutkowski; "On the Geometry of Interest Rate Models" by T. Björk; "Heterogeneous Beliefs, Speculation and Trading in Financial Markets" by J.A. Scheinkman, and W. Xiong.

From Probability to Finance

Author: Ying Jiao

Publisher: Springer

Published: 2021-03-21

Total Pages: 248

ISBN-13: 9789811515781

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This volume presents a collection of lecture notes of mini-courses taught at BICMR Summer School of Financial Mathematics, from May 29 to June 9, 2017. Each chapter is self-contained and corresponds to one mini-course which deals with a distinguished topic, such as branching processes, enlargement of filtrations, Hawkes processes, copula models and valuation adjustment analysis, whereas the global topics cover a wide range of advanced subjects in financial mathematics, from both theoretical and practical points of view. The authors include world-leading specialists in the domain and also young active researchers. This book will be helpful for students and those who work on probability and financial mathematics.