E-Book, Englisch, 357 Seiten
ISBN: 978-1-4398-6719-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
