Chapman and Hall/CRC
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
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.