Random Dynamical Systems in Finance

ISBN-13: 9780367380144 / Angielski / Miękka / 2019 / 357 str.

Anatoliy Swishchuk; Shafiqul Islam

Opis

With extensive end-of-chapter references, 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. Through numerous examples, the authors explain 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. They also develop techniques for implementing RDS as approximations to financial models and option pricing formulas.

Spis treści

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.

O autorze

Swishchuk, Anatoliy ; Islam, Shafiqul