General stochastic asset price models; classical stochastic volatility models (Hull-White, Stein-Stein, Heston); Gaussian Volterra type stochastic volatility models; fractional and rough models; scaling properties of 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 G\"{a}rtner-Ellis theorem.
Stochastic Processes
Non-homogeneous Markov processes, time-reversal and duality theory for Markov processes, applications of Markov processes to parabolic initial and final value problems.
Semigroup Theory and Propagator Theory
Schroedinger semigroups and Feynman-Kac propagators; non-autonomous Kato classes of functions and measures; smoothing properties of Schroedinger semigroups.
