Random Dynamical Systems in Finance

Anatoliy Swishchuk, Shafiqul Islam

April 23, 2013 by Chapman and Hall/CRC
Reference - 357 Pages - 35 B/W Illustrations
ISBN 9781439867181 - CAT# K13017

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Features

  • Represents the first book that contains applications of RDS in finance and economics
  • Develops approximations of European call option prices through various RDS
  • Discusses stability and optimal control of RDS
  • Describes delayed RDS with jumps and regime-switching

Summary

The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this emerging area, Random Dynamical Systems in Finance shows how to model RDS in financial applications.

Through numerous examples, the book explains how the theory of RDS can describe the asymptotic and qualitative behavior of systems of random and stochastic differential/difference equations in terms of stability, invariant manifolds, and attractors. The authors present many models of RDS and develop techniques for implementing RDS as approximations to financial models and option pricing formulas. For example, they approximate geometric Markov renewal processes in ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option pricing formulas.

With references at the end of each chapter, this book provides a variety of RDS for approximating financial models, presents numerous option pricing formulas for these models, and studies the stability and optimal control of RDS. The book is useful for researchers, academics, and graduate students in RDS and mathematical finance as well as practitioners working in the financial industry.