Introduction to Markov Processes and Their Applications

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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 in-depth 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 continuous-time 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 Stroock-Varadhan, 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 One-dimensional diffusions

Lecture Notes on Filtering

Problem Set 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

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London School of Economics and Political Science 2013