Umut’s research falls into the field of stochastic analysis, often with an applied emphasis on understanding the imperfections in financial markets. More recently his research has movedtowards equilibrium analysis in Market Microstructure Theory, especially in the presence of asymmetric information. Analysis of such models leads to interesting inverse problems in Markov processes theory and one needs to apply a combination of various techniques from stochastic filtering, stochastic and partial differential equations, conditioning of Markov processes, and the theory of enlargement of filtrations.
Although there is a vast amount of works in the economics literature on market microstructure, they often lack the sufficient level of generality to be applied safely to today's highly complex financial markets. The necessity of having a more general and robust model becomes more paramount when one considers the fact that a good market microstructure model is the basis for answering questions related to market design and regulation. However, such extensions have not so far been adequately dealt with in the literature due to the technical difficulties involved with equilibrium in a general framework. A typical challenge that arise in this field is the construction of realistic yet tractable equilibrium models that capture the impacts of specific trading mechanisms and the heterogeneity of traders. Umut’s recent research has extended the available theory in many ways by incorporating more general private signals, default risk and risk aversion.