Deterministic And Stochastic Topics In Computational Finance

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Deterministic And Stochastic Topics In Computational Finance

Ovidiu Calin
Deterministic And Stochastic Topics In Computational Finance Book PDF

Author : Ovidiu Calin
Publisher : World Scientific Publishing Company
Page : 484 pages
File Size : 52,8 Mb
Release : 2016-11-25
Category : Business & Economics
ISBN : 9789813203105

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Deterministic And Stochastic Topics In Computational Finance by Ovidiu Calin Pdf

What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:

Mathematical Finance

Jacques Janssen,Raimondo Manca,Ernesto Volpe
Mathematical Finance Book PDF

Author : Jacques Janssen,Raimondo Manca,Ernesto Volpe
Publisher : John Wiley & Sons
Page : 584 pages
File Size : 51,6 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9781118622414

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Mathematical Finance by Jacques Janssen,Raimondo Manca,Ernesto Volpe Pdf

This book provides a detailed study of Financial Mathematics. In addition to the extraordinary depth the book provides, it offers a study of the axiomatic approach that is ideally suited for analyzing financial problems. This book is addressed to MBA's, Financial Engineers, Applied Mathematicians, Banks, Insurance Companies, and Students of Business School, of Economics, of Applied Mathematics, of Financial Engineering, Banks, and more.

Stochastic Analysis, Filtering, and Stochastic Optimization

George Yin,Thaleia Zariphopoulou
Stochastic Analysis Filtering and Stochastic Optimization Book PDF

Author : George Yin,Thaleia Zariphopoulou
Publisher : Springer Nature
Page : 466 pages
File Size : 43,5 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.

Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes

Cornelis W Oosterlee,Lech A Grzelak
Mathematical Modeling And Computation In Finance With Exercises And Python And Matlab Computer Codes Book PDF

Author : Cornelis W Oosterlee,Lech A Grzelak
Publisher : World Scientific
Page : 1310 pages
File Size : 40,7 Mb
Release : 2019-10-29
Category : Business & Economics
ISBN : 9781786347961

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Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes by Cornelis W Oosterlee,Lech A Grzelak Pdf

This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact [email protected].

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)

Ovidiu Calin
Informal Introduction To Stochastic Calculus With Applications An Second Edition Book PDF

Author : Ovidiu Calin
Publisher : World Scientific
Page : 510 pages
File Size : 40,6 Mb
Release : 2021-11-15
Category : Mathematics
ISBN : 9789811247118

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Informal Introduction To Stochastic Calculus With Applications, An (Second Edition) by Ovidiu Calin Pdf

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.

Stochastic Geometric Analysis With Applications

Ovidiu Calin
Stochastic Geometric Analysis With Applications Book PDF

Author : Ovidiu Calin
Publisher : World Scientific
Page : 557 pages
File Size : 50,9 Mb
Release : 2023-11-21
Category : Mathematics
ISBN : 9789811283291

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Stochastic Geometric Analysis With Applications by Ovidiu Calin Pdf

This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.

Stochastic Calculus for Quantitative Finance

Alexander A Gushchin
Stochastic Calculus for Quantitative Finance Book PDF

Author : Alexander A Gushchin
Publisher : Elsevier
Page : 208 pages
File Size : 55,8 Mb
Release : 2015-08-26
Category : Mathematics
ISBN : 9780081004760

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Stochastic Calculus for Quantitative Finance by Alexander A Gushchin Pdf

In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance

Stochastic Analysis for Finance with Simulations

Geon Ho Choe
Stochastic Analysis for Finance with Simulations Book PDF

Author : Geon Ho Choe
Publisher : Springer
Page : 657 pages
File Size : 47,5 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 9783319255897

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Stochastic Analysis for Finance with Simulations by Geon Ho Choe Pdf

This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.

Handbook of Computational Finance

Jin-Chuan Duan,Wolfgang Karl Härdle,James E. Gentle
Handbook of Computational Finance Book PDF

Author : Jin-Chuan Duan,Wolfgang Karl Härdle,James E. Gentle
Publisher : Springer Science & Business Media
Page : 804 pages
File Size : 53,9 Mb
Release : 2011-10-25
Category : Business & Economics
ISBN : 3642172547

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Handbook of Computational Finance by Jin-Chuan Duan,Wolfgang Karl Härdle,James E. Gentle Pdf

Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Stochastic Calculus for Finance II

Steven Shreve
Stochastic Calculus for Finance II Book PDF

Author : Steven Shreve
Publisher : Springer
Page : 550 pages
File Size : 49,8 Mb
Release : 2010-12-01
Category : Mathematics
ISBN : 144192311X

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Stochastic Calculus for Finance II by Steven Shreve Pdf

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

Tools for Computational Finance

Rüdiger U. Seydel
Tools for Computational Finance Book PDF

Author : Rüdiger U. Seydel
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 50,8 Mb
Release : 2012-03-09
Category : Mathematics
ISBN : 9781447129936

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Tools for Computational Finance by Rüdiger U. Seydel Pdf

The disciplines of financial engineering and numerical computation differ greatly, however computational methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering; specifically the use of numerical methods as tools for computational finance. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its fifth edition, Tools for Computational Finance has been significantly revised and contains: A new chapter on incomplete markets which links to new appendices on Viscosity solutions and the Dupire equation; Several new parts throughout the book such as that on the calculation of sensitivities (Sect. 3.7) and the introduction of penalty methods and their application to a two-factor model (Sect. 6.7) Additional material in the field of analytical methods including Kim’s integral representation and its computation Guidelines for comparing algorithms and judging their efficiency An extended chapter on finite elements that now includes a discussion of two-asset options Additional exercises, figures and references Written from the perspective of an applied mathematician, methods are introduced as tools within the book for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate students in mathematics, engineering and other scientific disciplines as well as professionals in financial engineering.

An Introduction to Computational Finance

™mr U?ur
An Introduction to Computational Finance Book PDF

Author : ™mr U?ur
Publisher : Imperial College Press
Page : 315 pages
File Size : 55,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9781848161924

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An Introduction to Computational Finance by ™mr U?ur Pdf

Although there are several publications on similar subjects, this book mainly focuses on pricing of options and bridges the gap between Mathematical Finance and Numerical Methodologies. The author collects the key contributions of several monographs and selected literature, values and displays their importance, and composes them here to create a work which has its own characteristics in content and style.This invaluable book provides working Matlab codes not only to implement the algorithms presented in the text, but also to help readers code their own pricing algorithms in their preferred programming languages. Availability of the codes under an Internet site is also offered by the author.Not only does this book serve as a textbook in related undergraduate or graduate courses, but it can also be used by those who wish to implement or learn pricing algorithms by themselves. The basic methods of option pricing are presented in a self-contained and unified manner, and will hopefully help readers improve their mathematical and computational backgrounds for more advanced topics.Errata(s)Errata

Stochastic Calculus for Finance I

Steven Shreve
Stochastic Calculus for Finance I Book PDF

Author : Steven Shreve
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 50,6 Mb
Release : 2005-06-28
Category : Mathematics
ISBN : 0387249680

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Stochastic Calculus for Finance I by Steven Shreve Pdf

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

Computational Methods for Quantitative Finance

Norbert Hilber,Oleg Reichmann,Christoph Schwab,Christoph Winter
Computational Methods for Quantitative Finance Book PDF

Author : Norbert Hilber,Oleg Reichmann,Christoph Schwab,Christoph Winter
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 46,9 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9783642354014

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Computational Methods for Quantitative Finance by Norbert Hilber,Oleg Reichmann,Christoph Schwab,Christoph Winter Pdf

Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to Lévy, additive and certain classes of Feller processes. This book is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics.​

Recent Developments In Computational Finance: Foundations, Algorithms And Applications

Peter Kloeden,Thomas Gerstner
Recent Developments In Computational Finance Foundations Algorithms And Applications Book PDF

Author : Peter Kloeden,Thomas Gerstner
Publisher : World Scientific
Page : 480 pages
File Size : 45,8 Mb
Release : 2012-11-30
Category : Business & Economics
ISBN : 9789814436441

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Recent Developments In Computational Finance: Foundations, Algorithms And Applications by Peter Kloeden,Thomas Gerstner Pdf

Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses.The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.