Utilization of Stochastic Optimization and Equilibrium Models in Portfolio Selection and Energy Finance

Our research effort follows the current challenging problems of portfolio analysis and energy
finance. In particular, we shall investigate sparse robust portfolio selection problems with
non-smooth objectives and analyze the joint effects of sparsity and robustification using real
stock exchange data. Also, we shall attempt at modeling the price of emission allowances and
provide predictions of the auction revenues in the Czech Republic emissions market. Further,
we plan to analyze the strategic behavior of agents in the deregulated electricity markets. In all
three research areas, we shall investigate models which have a common general mathematical
structure. We plan to use the cutting-edge mathematical tools of variational analysis and apply
the state-of-the-art methods of nonsmooth and stochastic optimization for development of new
numerical techniques. We attempt at development of a new theory which has not yet been
reflected in the literature as well as of research studies based on real world instances.