This paper is dedicated to R.T. Rockafellar for his stimulating and impressive work in convex optimization for decades. We thank you for the insights and inspirations we gained from your fundamental research.

Risk management by applying operational flexibility is becoming a key issue for production companies. This paper discusses how a power portfolio can be hedged through its own production assets. In particular we model operational flexibility of a hydro pump storage plant and show how to dispatch it to hedge against adverse movements in the portfolio. Moreover, we present how volume risk, which is not hedgeable with standard contracts from power exchanges, can be managed by an intelligent dispatch policy. Despite the incompleteness of the market we quantify the value of this operational flexibility in the framework of coherent risk measures.

The finite differences value function of an American put option can be computed by solving a sequence of Linear Complementarity Problems (LCP). The state of the art methods that solve these equations converge slowly. Recently, Borici and Lüthi have shown that in the case of the implicit discretisation scheme it is possible to solve LCPs in a computer time which grows linearly with the number of spatial grid points. In this paper we show that this result can be generalised for the more accurate discretisation scheme of Crank-Nicolson. We give examples that illustrate this result.

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We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty's least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris's highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, all pivot rules require only a linear number of iterations. As the main tool, we employ unique-sink orientations of cubes, a useful combinatorial abstraction of the P-LCP.