Instructor: Elena Kosygina
First examples of stochastic processes and an informal introduction of basic notions and tools.
- Random walks. Gambler’s ruin
- Pricing by arbitrage. The binomial asset pricing model
- Real-world and risk-neutral probabilities
- Poisson processes
Measure-theoretic language and essential background
- Weak convergence
- Laws of large numbers and the central limit theorem
- Conditional expectations
- Martingales. Stopping times. Optional stopping theorem
- Brownian Motion
Instructor’s Notes were distributed at each class.