This project is devoted to the study of stochastic control problems with possible applications ranging from energy and power systems to economics and finance. In particular, we are interested in the theoretical and numerical study of optimal strategies in one of the following classes of problems:
* Optimal stopping problems. These can be used to design, price and hedge contracts with features similar to those of American type options.
* Irreversible (partially reversible) investment problems. These find numerous applications in the study of real options and energy systems.
* Zero-sum and nonzero-sum games of control and stopping. These games are well-suited to model situations where multiple agents compete or cooperate to achieve certain goals; hence they can be used to describe financial markets and energy markets.
Versions of the above problems featuring also partial and asymmetric information may be considered. The methodologies that will be used in this project are inspired by stochastic calculus, stochastic differential equations and partial differential equations. It is therefore expected that applicants have a strong background in one or more of those areas of mathematics.
The Financial Mathematics group in Leeds has strong expertise in stochastic control and stochastic analysis. As a PhD student in our group you will have the opportunity to interact with several other young researchers in this area and you will benefit from frequent scientific visits of leading international academics in the field.