Stochastic Processes with Applications to Finance

Masaaki Kijima

286 pages, parution le 28/11/2002

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Résumé

In recent years, modeling financial uncertainty using stochastic processes has become increasingly important, but it is commonly perceived as requiring a deep mathematical background. Stochastic Processes with Applications to Finance shows that this is not necessarily so. It presents the theory of discrete stochastic processes and their applications in finance in an accessible treatment that strikes a balance between the abstract and the practical.

Using an approach that views sophisticated stochastic calculus as based on a simple class of discrete processes-"random walks"-the author first provides an elementary introduction to the relevant areas of real analysis and probability. He then uses random walks to explain the change of measure formula, the reflection principle, and the Kolmogorov backward equation. The Black-Scholes formula is derived as a limit of binomial model, and applications to the pricing of derivative securities are presented. Another primary focus of the book is the pricing of corporate bonds and credit derivatives, which the author explains in terms of discrete default models.

By presenting important results in discrete processes and showing how to transfer those results to their continuous counterparts, Stochastic Processes with Applications to Finance imparts an intuitive and practical understanding of the subject. This unique treatment is ideal both as a text for a graduate-level class and as a reference for researchers and practitioners in financial engineering, operations research, and mathematical and statistical finance.

Contents

Elementary Calculus: Towards Ito's Formula
Elements in Probability
Useful Distributions in Finance
Derivative Securities
A Discrete-time model for securities market
Random Walks
The Binomial Model
A Discrete-Time Model for Defaultable Securities
Markov Chains
Monte Carlo Simulation
From Discrete to Continuous: Towards the Black-Scholes
Basic Stochastic Processes in Continuous Time
A Continuous-Time Model for Securities Market

L'auteur - Masaaki Kijima

University of Kyoto,Kyoto, Japan

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Masaaki Kijima
Parution	28/11/2002
Nb. de pages	286
Format	15,8 x 24,2
Couverture	Relié
Poids	527g
Intérieur	Noir et Blanc
EAN13	9781584882244
ISBN13	978-1-58488-224-4