Stochastic optimization with dynamic probabilistic forecasts

We consider a sequential decision making process such as energy trading or electrical production scheduling whose outcome depends on the future realization of a random factor, such as a meteorological variable. Assuming that the decision maker has access to a dynamically updated probabilistic forecast (predictive distribution) of the random factor, we propose several stochastic models for the evolution of the probabilistic forecast of a given quantity, and show how these models may be calibrated from ensemble forecasts, commonly provided by weather centers. We then show how these stochastic models can be used to determine optimal decision making strategies to maximize a specific gain functional. Applications to wind energy trading are given.