Distributionally robust optimization with multiple time scales: valuation of a thermal power plant

The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. However, also this approach has its limitations, since quite often the models for costs and revenues are subject to model error. Under a prudent valuation, the possible model error should be incorporated into the calculation. In this paper, we consider the valuation of a power plant under ambiguity of probability models for costs and revenues. The valuation is done by stochastic dynamic programming and on top of it, we use a dynamic ambiguity model for obtaining the prudent minimax valuation. For the valuation of the power plant under model ambiguity we introduce a distance based on the Wasserstein distance. Another highlight of this paper is the multiscale approach, since decision stages are defined on a weekly basis, while the random costs and revenues appear on a much finer scale. The idea of bridging stochastic processes is used to link the weekly decision scale with the finer simulation scale. The applicability of the introduced concepts is broad and not limited to the motivating valuation problem.