1. Random variables, Conditional probability and Conditional expectation Review of probability basics; Baye‘s theorem; Computing probabilities and expectations by conditioning; Applications and examples 2. Markov chains State definition, transition probabilities; Chapman-Kolmogorov equation; Steady state probabilities Applications and examples 3. Continuous time Markov chains Birth-death processes; Limiting probabilities; Applications and examples 4. Renewal reward theory Renewal reward processes; Insurance ruin problem; Other applications and examples 5. Brownian motion process and financial option pricing Hitting times; Gambler‘s ruin problem; Geometric Brownian motion process; Pricing stock options
- Teacher: rrmarathe RAHUL MARATHE