Markov Processes in Finance

Course Description

This course will motivate a solid foundation in the theory of Markov processes with numerous applications in finance. Applications will be taken from: mortgage modeling, credit modeling, dynamic programming, Monte Carlo Markov chain and Hidden Markov Models. Theory will be taken from: stationary distributions, quasi-stationary distributions, absorption probabilities, convergence, statistical modeling, etc. We will focus will be primarily on finite Markov chains but also discuss various divergences from this type of model. The class will place emphasis on mathematics and statistical modeling.

Pre-requisites

Linear Algebra
Calculus
Elementary Probability Theory

Instructor

Kevin Atteson
ksa236@nyu.edu
http://atteson.com/Markov/Markov.html

Grading

1 Pre-midterm Homework Assignment 25%
1 Midterm Exam 25%
1 Pre-final Homework Assignment 25%
1 Final Exam 25%

Syllabus

Lecture 1 (September 4):	Mortgage models of default and absorption probabilities
Lecture 2 (September 11):	Elementary probability, conditional probability, independence
	Some linear algebra
	Classification of states, stationary distributions and convergence
Lecture 3 (September 18):	Probability densities and expected values
Lecture 4 (September 25):	Fitting Markov chains
Lecture 5 (October 2):	Markov chains in credit modeling (homework distributed)
Lecture 6 (October 9):	Algorithms and dynamic programming (homework collected)
Lecture 7 (October 16):	Homework discussions
Lecture 8 (October 23):	Midterm Exam
Lecture 9 (October 30):	Hidden Markov models, Expectation Maximization and regime-switching models (homework discussed)
Lecture 10 (November 6):	Optimal trading strategies
Lecture 11 (November 13):	Bayesian analysis and Markov Chain Monte Carlo (homework distributed)
Lecture 12 (November 20):	Markov Chain Miscellanea (homework collected)
Lecture 13 (December 4):	Homework discussions
Lecture 14 (December 11):	Final Exam