Random Dynamical Systems in Finance

Anatoliy Swishchuk, Shafiqul Islam

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English

Chapman & Hall/CRC
23 September 2019

Economic systems & structures; Probability & statistics; Applied mathematics; Computer security

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.

By: Anatoliy Swishchuk, Shafiqul Islam
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367380144
ISBN 10: 0367380145
Pages: 357
Publication Date: 23 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction. Deterministic Dynamical Systems and Stochastic Perturbations. Random Dynamical Systems and Random Maps. Position-Dependent Random Maps. Random Evolutions as Random Dynamical Systems. Averaging of the Geometric Markov Renewal Processes (GMRP). Diffusion Approximations of the GMRP and Option Price Formulas. Normal Deviation of a Security Market by the GMRP. Poisson Approximation of a Security Market by the GMRP. Stochastic Stability of Fractional RDS in Finance. Stability of RDS with Jumps in Interest Rate Theory. Stability of Delayed RDS with Jumps and Regime-Switching in Finance. Optimal Control of Delayed RDS with Applications in Economics. Optimal Control of Vector-Delayed RDS with Applications in Finance and Economics. RDS in Option Pricing Theory with Delayed/Path-Dependent Information. Epilogue. Index.

Swishchuk, Anatoliy ; Islam, Shafiqul

Reviews for Random Dynamical Systems in Finance

.. . the timely publication of this book is very welcome and appreciated. There are not many books on RDS, and as far as this reviewer knows, this book is the only one that deals with the application of RDS in finance. ... There are many examples from finance, and it is very interesting to see that classical problems in finance, such as pricing European call-options, are interpreted in the viewpoint of RDS. Overall, this is a very useful book to both researchers of RDS and financial engineers ... --Mathematical Reviews, November 2014