Stochastic Analysis And Applications To Finance
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Stochastic Processes with Applications to Finance
Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools
Stochastic Calculus and Financial Applications
Author: J. Michael Steele
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance. The Wharton School course that forms the basis for this book is designed for energetic students who have had some experience with probability and statistics but have not had ad vanced courses in stochastic processes. Although the course assumes only a modest background, it moves quickly, and in the end, students can expect to have tools that are deep enough and rich enough to be relied on throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more de manding development of continuous-time stochastic processes, especially Brownian motion. The construction of Brownian motion is given in detail, and enough mate rial on the subtle nature of Brownian paths is developed for the student to evolve a good sense of when intuition can be trusted and when it cannot. The course then takes up the Ito integral in earnest. The development of stochastic integration aims to be careful and complete without being pedantic.
Option Theory with Stochastic Analysis
Author: Fred Espen Benth
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.