MTH 9831 Probability and Stochastic Processes for Finance I
Downloads:
- Detailed Syllabus
- Homeworks: HW2; HW11
- Final Exam
Instructor: Elena Kosygina
Topics:
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.
Reference Books:
- Mathematical Techniques in Finance: Tools for Incomplete Markets, A. Cerny
- A Course in Financial Calculus, A. Etheridge
- Probability Essentials, J. Jacod, Ph. Protter
- Probability, A. N. Shiryaev
- Stochastic Calculus for Finance I, II, S. Shreve