Stochastic Processes 2025

Logistics

Timings: Monday and Friday at 9:30 AM

Teaching Assistants: Nikhil Rajan, Akila Hariharan and Rithenya Rhevani

Syllabus

Introduction to Discrete time Markov chains: Definition, examples. Chapman-Kolmogorov equation. Absorbing state theory. State structure of finite state markov chains, theorems on transience and positive recurrence, ergodic and stationary properties.

Introduction to probability space and partition sigma algebras (discrete random variables). Conditional expectation with respect to sigma algebras.

Martingales and the basic theorems motivated by gambling. Relations between DTMC and martingales via potential theory.

Finance: Expected utility, risk profiles of agents and derivations of fundamental pricing equations in finance (Cochrane and Lucas views). Martingale Asset pricing theorem with proof.

Course Notes

Since there are very few books that integrate macroeconomics and finance applications into a stochastic process course, I have typed up some notes. I am working on these notes and they are far from complete. So use it at your own peril: Srikanth Pai’s Course Notes (in progress)

Course Objectives

The course introduces undergraduates to probability theory and random processes, with an emphasis on methods used to analyze dynamic phenomena in economics and finance. The objective is twofold: (i) to equip students with the mathematical tools to identify and characterize the essential properties of stochastic processes, and (ii) to train them to compute and interpret quantities of interest such as expectations, distributions, and limiting behaviors. Alongside the theory, students will read and analyze classic papers in economics and finance where stochastic methods play a central role, in order to see how abstract tools are applied in frontier research.

References

• Sheldon M. Ross; “Introduction to Probability Models”, Academic Press, Ninth Edition, 2007.
• Brzezniak and Zastawniak; “Basic Stochastic Processes”, Springer, Second Indian Reprint, 2009.

Assignments

• Week 1
• Week 2
• Week 3
• Week 4
• Week 5
• No Week 6 HW due to internals.
• Week 7
• Week 8 and 9 - homeworks from lecture notes.
• Week 10
• Week 11 and 12 - homeworks from lecture notes.

Main Tests

• Internal I: Students were tested on Discrete-time Markov chains.
• For Internals II, students had to present a paper on DTMC or Martingales. The projects reports of students will be displayed here.