Selected Problems of Stochastic Optimisation under Uncertainty

In this work, we analyse heavy tailed distributions with most emphasis on stable distributions, deal with stochastic dominance, and apply these results in optimisation problems which arise from gas storage valuation. We use stochastic dynamic programming for solving this problem and deal with different price models, such as discretised price model with the stable transition matrix estimated from observations, Ornstein-Uhlenbeck, AR(1)- GARCH(1,1) models, etc. We take into account the feature that some European gas storage units are connected to several markets and translate it into our optimisation procedures. We also explore the role of tails in the problem of gas storage valuation and offer approaches for including stochastic dominance constraints.