This paper provides a set of stochastic multistage programs where the evolvement of uncertain factors is given by stochastic processes. We treat a practical problem statement within the field of managing fixed-income securities. Detailed information on the used parameter values in various interest rate models is given. Barycentric approximation is applied to obtain computational results; different measures of the achieved goodness of approximation are indicated.
Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are ? up to a certain size ? easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ? based on the solutions at the previous ?-1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).
Unsicherheiten im Strommarkt erfordern flexible Reaktionen von Stromversorgungsunternehmen auf sich kontinuierlich wandelnde Strukturen. Marktteilnehmer ohne marktbeherrschende Stellung müssen zunehmend die kurzfristig hochvolatilen und langfristig nicht prognostizierbaren Preisentwicklungen berücksichtigen. Federführend durch die Stadtwerke Giessen AG und motiviert durch ihre konzeptionellen Herausforderungen im Tagesgeschäft hat das ior/cf-HSG gemeinsam mit der österreichischen Energieberatungsgesellschaft Verbundplan GmbH ein leistungsfähiges Portfoliomanagementsystem auf Basis stochastischer Optimierung entwickelt. Es bietet eine anpassungsfähige Ergänzung zu herkömmlichen Ansätzen und integriert ein innovatives Risikomanagement. Neue Bewertungsansätze für komplexe Derivate reduzieren darüber hinaus das Modellrisiko gegenüber traditionellen Methoden.
In the electric power industry the observed increases of electricity price dynamics combined with the characteristic periodicity of related decision processes have motivated the use of multistage stochastic programming in recent years to provide flexible models for practical applications in the sector. Specifically in power generation and trading the planning process must obey highly complex interrelations between manifold influences. They range from short term price fluctuations as observed in spot markets to long term changes of fundamental influences. Not only changes in the electric supply system itself must be considered, but also the related availability and costs of required fuels. For example, the prices and usability of natural gas in power generation also depend on the existence of respective deployment and distribution systems. Furthermore the electric power sector is exposed to manifold regulatory uncertainties related to the rules imposed by the responsible authorities. Recently environmental issues have become very popular due to the ongoing discussion on climate change. In January 2005 the European Emissions Trading Scheme (EU ETS) has been launched which by many is considered a new key element in efficient electricity market operations. In this paper we will introduce a modeling framework that considers the influence of emission trading on portfolio problems in the electric power sector by applying clean valuation schemes that particularly take fuel costs, emission efficiency in combination with investment possibilities and generation flexibility into account. Sensitivity analysis is performed with respect to changes in technology, volatilities and price scenarios.
