Random dynamical systems in finance (Q2839192)

Random dynamical systems (RDS) have especially been studied in many contest in economics, particularly in modeling 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. RDS 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 the ergodic, merged, double-averaged, diffusion, normal deviation, and Poisson cases and apply the obtained results to option formulas. This book provides a variety of RDS for approximating financial models, and studies the stability and optimal control of RDS. The book is useful for graduate students in RDS and mathematical finance as well as practitioners working in the financial industry.