Analysis of longitudinal data, in particular survival analysis and inference in time series and differential equations, with application to finance. Stochastic simulation. Design of experiments. Observational studies.
Finance and economics, in particular financial econometrics, and the pricing and hedging of derivative securities. High frequency data. Risk management. The interface between statistical uncertainty and prices, especially how to hedge against statistical uncertainty. Incomplete markets.
The application of likelihood theory to martingales, and vice versa. Nonparametric likelihood. Methods for analyzing and improving on asymptotic approximations to sampling distributions, including likelihood methods, asymptotic expansions (Edgeworth, saddlepoint) and resampling (bootstrapping, jackknifing).