Hans-Jakob Lüthi

Risk management of power portfolios and valuation of flexibility

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.

Risk management in power markets: The Hedging value of production flexibility

Since the 1990s power markets are being restructured worldwide and nowadays electrical power is traded as a commodity. The liberalization and with it the uncertainty in gas, fuel and electrical power prices requires an effective management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. The challenge for participants in the newly competitive market environment is how to design, price and hedge derivative contracts in particular combination with the flexibility embedded in dispatch strategies of production assets. Accordingly, an adequate basis for management and investment decisions is needed which responds to the highly complex market situation.

Fast Solutions of Complementarity Formulations in American Put Pricing

The finite-difference value function of an American put option can be computed by solving a sequence of linear complementarity problems (LCPs). The state-of-the-art methods that solve these equations converge slowly. Recently, Borici and Luthi have shown that in the case of the implicit discretization 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 generalized for the more accurate discretization scheme of Crank and Nicolson. We give examples that illustrate this result.

Pivoting in Linear Complementarity: Two Polynomial-Time Cases

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.

The Regularization Aspect of Optimal-Robust Conditional Value-at-Risk Portfolios

In portfolio management, Robust Conditional Value - at - Risk (Robust CVaR) has been proposed to deal with structured uncertainty in the estimation of the assets probability distribution. Meanwhile, regularization in portfolio optimization has been investigated as a way to construct portfolios that show satisfactory out-ofsample performance under estimation error. In this paper, we prove that optimal- Robust CVaR portfolios possess the regularization property. Based on expected utility theory concepts, we explicitly derive the regularization scheme that these portfolios follow and its connection with the scenario set properties.

On Value of Flexibility in Energy Risk Management. Concepts, Models, Solutions

Since 90s power markets are being restructured worldwide and nowadays electrical energy is traded as a commodity. Therewith the question how to manage and hedge the financial risks resulting from uncertain electrical power and fuel prices is essential for market participants. There exists a rich literature on risk management in energy markets. Some noteworthy references can be downloaded from our web resources [1] and are reviewed in the cited literature. Let us first investigate the market structure and then discuss two different pricing schemes for risk management in power industries.

Linear complementarity problem with upper bounds

Abstract The problem addressed in this paper is the linear complementarity problem with upper bounds. First we show, using only combinatorial arguments, that the number of solutions is odd. Secondly a variable dimension algorithm based on complementary pivoting is given to find such a solution.

Computer-Laien als Experten?

Die vorliegende Arbeit soll aufzeigen, wie mittels Benutzerpartizipation bei der Entwicklung und Evaluation von Programmsystemen arbeitspsychologischen Kriterien angepasste und damit fur den Benutzer adaquate Systeme erzeugt werden konnen. Die verwendete Organisation und die programmiertechnischen Verfahren beim Design, bei der Implementierung und bei der Evaluation werden beschrieben. Anhand von ausgewahlten Beispielen wird aufgezeigt, wie die in Experimenten gewonnenen Erkenntnisse uber die Denkweise von Benutzern das Systemdesign verandern und verbessern.

Der Fixpunktsatz von Brouwer

Stetige Abbildungen kompakter konvexer Mengen in sich haben die wichtige Eigenschaft, dass sie einen Fixpunkt besitzen.

Geometrische Interpretation des linearen Komplementaritätsproblems

Sowohl das Komplementaritatsproblem wie auch der Lemke-Algorithmus lassen sich geometrisch anschaulich interpretieren.