Random variables and stochastic processes. Discrete time Markov chains (DTMC). Classification. Stationary distribution. Random walks. Simple applications of DTMC's. Counting processes and Poisson Processes. Non-homogeneous PP and Compound PP. Branching processes.
A simple market model. Risk-Free Assets. Risky Assets. Discrete Time Market Models. Portfolio Management. Brownian Motion. Stochastic differential equations. Elementary Itô calculus. The Black Scholes model.
