1. Introduction -- 2. Deterministic dynamical systems and stochastic perturbations -- 3. Random dynamical systems and random maps -- 4. Position dependent random maps -- 5. Random evolutions as random dynamical systems -- 6. Averaging of the Geometric Markov Renewal Processes (GMRP) -- 7. Diffusion approximations of the GMRP and option price formulas -- 8. Normal deviation of a security market by the GMRP -- 9. Poisson approximation of a security market by the Geometric Markov Renewal Processes -- 10. Stochastic stability of fractional RDS in finance -- 11. Stability of RDS with jumps in interest rate theory -- 12. Stability of delayed RDS with jumps and regime-switching in finance -- 13. Optimal control of delayed RDS with applications in economics -- 14. Optimal control of vector delayed RDS with applications in finance and economics -- 15. RDS in option pricing theory with delayed/path-dependent information -- 16. Epilogue.