LSE Statistics - Umut Cetin

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 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