This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.

Author: David C. Heath Glen SwindlePublish On: 2000-01-25

Volume 57 , 1999 An Introduction to Option Pricing and the Mathematical Theory of Risk Marco Avellaneda This review paper discusses the topic of option pricing with emphasis on modeling financial risk . The Black - Scholes formula is ...

Author: David C. Heath Glen Swindle

Publisher: American Mathematical Soc.

ISBN: 0821867628

Category:

Page:

View: 458

The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Theorie de la speculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought remarkable and important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and growth. Concurrently with these mathematical advances, markets have grown, and developments in both academia and industry continue to expand. This lively activity inspired an AMS Short Course at the Joint Mathematics Meetings in San Diego (CA). The present volume includes the written results of that course. Articles are featured by an impressive list of recognized researchers and practitioners. Their contributions present deep results, pose challenging questions, and suggest directions for future research. This collection offers compelling introductory articles on this new, exciting, and rapidly growing field.

Math. Finance 16(2), 237–254 (2006) E. Eberlein, W. Kluge, Calibration of Lévy term structure models, in Advances in Mathematical Finance (Birkhäuser, Boston, 2007), pp. 147–172 E. Eberlein, F. Özkan, The defaultable Lévy term ...

Author: Ernst Eberlein

Publisher: Springer Nature

ISBN: 9783030261061

Category: Mathematics

Page: 772

View: 543

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.

This leads to research in quantitative tools based on mathematical methods, i.e. the theory of Mathematical Finance. Especially since the pioneer work of Black, Scholes and Merton in the 70's, there is an explosive growth of the study ...

Author: Siu-Ah Ng

Publisher: World Scientific

ISBN: 9789810244286

Category: Business & Economics

Page: 298

View: 676

At the beginning of the new millennium, two unstoppable processes are taking place in the world: (1) globalization of the economy; (2) information revolution. As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives. Hence there is a need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance.Ever since the pioneer work of Black, Scholes and Merton in the 70's, there has been rapid growth in the study of mathematical finance, involving ever more sophisticated mathematics. However, from the practitioner's point of view, it is desirable to have simpler and more useful mathematical tools.This book introduces research students and practitioners to the intuitive but rigorous hypermodel techniques in finance. It is based on Robinson's infinitesimal analysis, which is easily grasped by anyone with as little background as first-year calculus. It covers topics such as pricing derivative securities (including the Black-Scholes formula), hedging, term structure models of interest rates, consumption and equilibrium. The reader is introduced to mathematical tools needed for the aforementioned topics. Mathematical proofs and details are given in an appendix. Some programs in MATHEMATICA are also included.

The main goal of the classical mathematical finance is to study the financial transactions. Therefore the main object of the traditional financial mathematics is the formalization of the exchange between monetary amounts that are ...

Author: Silvia Romagnoli

Publisher: Società Editrice Esculapio

ISBN: 9788874889747

Category: Business & Economics

Page: 416

View: 525

The aim of these two books is to provide the basic theoretical concepts and the best practice concerning the mathematical nance which is unescapable to understand the way modern financial markets operate. Thanks to these fundamental concepts, which are completely concentrated on a deterministic modelization of the markets, students are ready to approach more advanced courses focused on the modern area of financial math where the deterministic assumption is left and stochastic assumptions concerning the evolution of the involved variables are included.

consequent undergraduate or graduate modules such as Mathematical Finance, Statistical Finance, and Stochastic Analysis; for undergraduate modules, some partscan be skipped. Respectively,theset ofproblemsprovided issufficient to cover ...

Author: Nikolai Dokuchaev

Publisher: Routledge

ISBN: 9781134121977

Category: Business & Economics

Page: 208

View: 796

Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of stochastic analysis and statistical finance that are covered in the majority of university programmes. Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes: an introduction to probability theory a detailed study of discrete and continuous time market models a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing a detailed discussion of options and their pricing, including American options in a continuous time setting. An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.

Of particular interest to Samuelson was the 'stochastic calculus' introduced by Japanese mathematician Kiyosi Itó. It is a curious fact that the mathematical theories relevant to finance came from the purest of pure mathematics rather ...

Author: Mark H. A. Davis

Publisher: Oxford University Press, USA

ISBN: 9780198787945

Category: BUSINESS & ECONOMICS

Page: 133

View: 900

Now a vital part of modern economies, the rapid growth of the finance industry in recent decades is largely due to the development of mathematical methods such as the theory of arbitrage. Asset valuation, credit trading, and fund management, now depend on these mathematical tools. Mark Davis explains the theories and their applications.

In this editorial, we tell authors the ideas on what types of papers we will accept for publication in the area of mathematical finance. We will discuss some well-cited papers of mathematical finance. Keywords: mathematics; probability ...

Author: Wing-Keung Wong

Publisher: MDPI

ISBN: 9783039435739

Category: Business & Economics

Page: 232

View: 600

Mathematical finance plays a vital role in many fields within finance and provides the theories and tools that have been widely used in all areas of finance. Knowledge of mathematics, probability, and statistics is essential to develop finance theories and test their validity through the analysis of empirical, real-world data. For example, mathematics, probability, and statistics could help to develop pricing models for financial assets such as equities, bonds, currencies, and derivative securities.

In Financial Mathematics, Springer Lecture Notes in Mathematics, Vol 1656, W. Runggaldier, Ed. Springer Verlag, 2001. 5. BJ ̈ORK, T., AND CRISTENSEN, B. Interest rate dynamics and consistent forward rate curves. Mathematical Finance 9 ...

Author: Tomasz R. Bielecki

Publisher: Springer

ISBN: 9783540444688

Category: Mathematics

Page: 254

View: 254

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.

Just as a modern society needs mechanical and electrical engineers to apply the principles of science and mathematics to build and maintain our mechanical and electronic systems, a world increasingly built on finance needs financial ...

Author: Arlie O. Petters

Publisher: Springer

ISBN: 9781493937837

Category: Mathematics

Page: 483

View: 675

This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.