Introduction to Markov Processes and Their Applications


Course summary:
This is an introduction to the theory of Markov processes and
their applications in finance. The course rigorously develops the basic
theory and offers an indepth analysis of diffusions processes and
their properties. The theoretical lectures are further supported by
weekly classes devoted mainly to the computational aspects of the
theory. A good understanding of martingales in continuoustime and Ito
integration theory will be assumed
The following topics will be covered:
Markov property and transition functions;
Feller processes;
Strong Markov property;
Martingale problem of StroockVaradhan, stochastic
differential equations, and their connection with partial differential
equations;
Diffusion processes;
One dimensional diffusions;
Selection of topics from filtering;
Optimal stopping and statistics of diffusion processes;
Applications to financial economics
Indicative reading:
Karatzas and S. Shreve: Brownian Motion and Stochastic Calculus. Springer
D. Revuz and M. Yor: Continuous Martingales and Brownian Motion. Springer
K.L. Chung and. J. Walsh: Markov Processes, Brownian Motion and Time Symmetry. Springer
Course material:
Please check this page regularly for the lecture notes, problem sets and
announcements.
Lecture Notes on Markov and Feller Property
Lecture Notes on Infinitesimal Generators
Lecture Notes on Martingale Problems and SDEs
Lecture Noteds on Onedimensional diffusions
Lecture Notes on Filtering
Problem Set 1
Solutions
Problem Set 2
Solutions
Problem Set 3
Solutions
Problem Set 4
Solutions
Problem Set 5
Solutions
Problem Set 6
Solutions
Problem Set 7
Solutions
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