My research is in two different areas of mathematics: complex analysis (including complex dynamics) and financial mathematics.
In complex analysis/dynamics, much of my current research is joint with Charles Favre (CNRS, Paris) and tries to use an algebraic concept (valuations) to study local data in the context of complex analysis (singularities of plurisubharmonic functions) and complex dynamics (degree growths under iterations).
On the financial mathematics side, I am working with Ronnie Sircar (Princeton) on applying a fast-mean reverting stochastic volatility models to utility maximization problems and pricing of exotic options. Another set of projects is joint with Jussi Keppo (UM IOE) where we study option pricing/hedging and game equilibria in tractable models of an illiquid financial market.
