Inference and Risk

I have been interested in parameter inference for diffusion-type processes in the past. Both continuous and discrete observation schemes have been of interest for me. I have now revived my work in this area.

Another area of interest is non-parametric inference for stationary ergodic Markov chains. I have shown an important local asymptotic minimax optimality result for the empirical distribution as an estimator of the stationary distribution of the chain. This result has many wide ranging consequences. In a more recent paper, it has also been applied to show how an efficient estimator of a linear functionals of Markov chains with parametric marginals can be constructed.

Studying dependence of random variables when their joint distribution is not multivariate normal is challenging but is very important in practice. A single correlation coefficient or a bunch of such coefficients is not enough to describe well the dependence in such cases and copula functions are a very useful tool. A particularly simple copula is the Archimedean copula. We have used spline methods in proposing an estimation procedure for Archimedean copulas that is numerically efficient for high dimensions and for large volumes of data.

I am also interested in Modelling Stochastic Risk with a particular focus on financial risk. Represenations of coherent risk measures and issues related to inference about such measures in static and in dynamic setting are both practically relevant and mathematically challenging.