ST922-15 Graduate Topics in Applied Probability and Mathematical Finance

Introductory description

This module runs in Term 2 and is core optional for first-year PhD students in the Warwick Centre for Doctoral Training in Statistics. Other PhD students should consult the module leader if they are interested in taking this module. This module is not available to undergraduate or postgraduate taught students.

The module will be comprised of three selected topics in the areas of applied probability or mathematical finance, which may change year to year.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Topics will vary from year to year. Example topics include:

• Nonlinear expectation and its application to model uncertainty.
• Backward stochastic differential equations (BSDEs) with quadratic growth and its application to utility maximization.
• Martingale Optimal Transport, the Skorokhod embedding problem and robust option pricing.
• The Merton problem and stochastic control.
• Risk Measures
• Stochastic population models.
• Random measures and Measure-valued process.
• Combinatorial stochastic processes and applications.
• Levy processes and self-similar Markov processes.
• Topics in spatial branching processes.
• A course on general Markov processes.
• Fragmentation and coalescent processes.
• Point processes and associated stochastic processes.
• Brownian motion and diffusion processes.
• Applications of stochastic processes in applied probability.
• Random matrices.
• Brownian motion and random media.
• Stochastic differential equations and Feynman-Kac formula.
• Brownian motion on Riemannian manifolds
• Introduction to Malliavin Calculus and Hörmander's theorem.
• Introduction to Large Deviation.
• Introduction to Stochastic PDEs.
• Hydrodynamics and Fluctuations for Statistical mechanics models.
• Introduction to Rough Paths.
• Interacting particle systems.
• Mixing times of Markov chains

Learning outcomes

By the end of the module, students should be able to:

• Demonstrate understanding of the main concepts, tools and ideas for each of the topics.
• Practice in presenting and explaining advanced mathematical topics.

Subject specific skills

Specific skills will depend on the topic but will broadly be the ability to understand the main concepts, tools and ideas in each of the topics.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.