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The paper considers a single utility company's long‐ and medium‐term hydropower planning. The uncertainties are from the electricity forward curve and a random inflow. A simple and intuitive parameterization is given for the optimal production strategy. The accuracy of the parameterization is analysed by comparing its expected cash flows with the corresponding upper bound. In a test case the proposed method is compared with the realized production strategy of a Norwegian hydropower producer during winters 1997–2003. The parameterization gives earnings that are within 2.6% from the theoretical upper bound. Further, the results illustrate that during some years, part of the realized production strategy can be explained with the method, suggesting that during these years the forward curve information has already been incorporated in the production planning. However, even during the years when the correlation between the proposed strategy and the realized production is low, the strategy would have increased t...

This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.

This paper derives a fixed risk level margin calculation model for a derivatives clearing house. The model enables the calculation of net margin requirements of customer's portfolios from the clearing house's perspective. First, the probability distribution of the value of the customer's portfolio is characterized. Second, the loss distribution of the clearing house is derived from this probability distribution and the default probability of the exchange member. Finally, the margin requirement of the investor is set based on the clearing house's loss distribution.