In this paper, we consider the problem of finding optimal portfolios in cases when the underlying probability model is not perfectly known. For the sake of robustness, a maximin approach is applied which uses a "confidence set" for the probability distribution. The approach shows the tradeoff between return, risk and robustness in view of the model ambiguity. As a consequence, a monetary value of information in the model can be determined.

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We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem is modeled as a Markov decision process of managing storage operation over time, for which we propose integrating stochastic dual dynamic programming with approximate dynamic programming. We show that the approximate solution converges towards an upper bound of the optimal solution. To demonstrate the efficiency of the solution approach, we fit an econometric model to actual price and inflow data and apply the approach to a case study of an existing hydro storage system. Our results indicate that the approach is tractable for a real-world application and that the gap between theoretical upper and a simulated lower bound decreases sufficiently fast.

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