Fields of Interest

Financial Mathematics:

General stochastic asset price models; classical stochastic volatility models (Hull-White, Stein-Stein, Heston); Gaussian models and models with reflection; fractional, rough, and super rough models; scaling properties of stochastic volatility models; sample path and small-noise large deviation principles for stochastic volatility models; models with jumps; option pricing theory; asymptotic behavior of stock price distribution densities, option pricing functions, and the implied volatility; moment explosions; geometrical methods in financial mathematics; Heston geometry; large and moderate deviation principles; the Gärtner-Ellis theorem.

Stochastic Processes:

Volterra Gaussian processes; non-homogeneous Markov processes; time-reversal and duality theory for Markov processes; applications of Markov processes to parabolic initial and final value problems; reflecting diffusions.

Semigroup Theory and Propagator Theory:

Schrödinger semigroups and Feynman-Kac propagators; non-autonomous Kato classes of functions and measures; smoothing properties of Schrödinger semigroups.