TY - CHAP
TI - Barycentric Bounds in Stochastic Programming: Theory and Application
T2 - Stochastic programming: the state of the art in honor of George B. Dantzig
UR - https://www.alexandria.unisg.ch/publications/21872
AU - Frauendorfer, K.
AU - Kuhn, D.
AU - Schürle, M.
PY - 2011
N2 - The design and analysis of efficient approximation schemes is of fundamental importance in stochastic programming research. Bounding approximations are particularly popular for providing strict error bounds that can be made small by using partitioning techniques. In this article we develop a powerful bounding method for linear multistage stochastic programs with a generalized nonconvex dependence on the random parameters. Thereby, we establish bounds on the recourse functions as well as compact bounding sets for the optimal decisions. We further demonstrate that our bounding methods facilitate the reliable solution of important real-life decision problems. To this end, we solve a stochastic optimization model for the management of non-maturing accounts and compare the bounds on maximum profit obtained with different partitioning strategies.
T3 - International Series in Operations Research and Management Science
PB - Springer Science+Business Media, LLC
CY - New York, NY
SN - 978-1-4419-1641-9
SP - 67
EP - 96
ER -
TY - JOUR
TI - Maximizing the net present value of a project under uncertainty
AU - Wiesemann, W.
AU - Kuhn, D.
AU - Rustem, B.
PY - 2010
N2 - We address the maximization of a project’s expected net present value when the activity durations and cash flows are described by a discrete set of alternative scenarios with associated occurrence probabilities. In this setting, the choice of scenario-independent activity start times frequently leads to infeasible schedules or severe losses in revenues. We suggest to determine an optimal target processing time policy for the project activities instead. Such a policy prescribes an activity to be started as early as possible in the realized scenario, but never before its (scenario-independent) target processing time. We formulate the resulting model as a global optimization problem and present a branch-and-bound algorithm for its solution. Extensive numerical results illustrate the suitability of the proposed policy class and the runtime behavior of the algorithm.
PB - Elsevier
CY - Amsterdam
SN - 0377-2217
JF - European Journal of Operational Research
VL - 2
IS - 202
SP - 356
EP - 367
ER -
TY - JOUR
TI - Analysis of the rebalancing frequency in log-optimal portfolio selection
AU - Kuhn, D.
AU - Luenberger, D. G.
PY - 2010
N2 - In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems in a Black-Scholes type economy which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We argue that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. Our analysis also reveals that diversification has a dual effect on the mean and variance of the portfolio growth rate as well as on their sensitivities with respect to the rebalancing frequency.
PB - Routledge
CY - Milton Park, UK
SN - 1469-7688
JF - Quantitative Finance
VL - 2
IS - 10
SP - 221
EP - 234
ER -
TY - JOUR
TI - An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time
AU - Kuhn, D.
PY - 2009
N2 - Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vectors are inherently difficult to solve. In fact, scenario tree-based algorithms are unsuitable for problems with many stages, while dynamic programming-type techniques are unsuitable for problems with many state variables. This paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time, thus having an extremely large (i.e., uncountable) number of decision stages. By perturbing the underlying data and information processes, we construct two approximate problems that provide bounds on the optimal value of the original problem. Moreover, we prove that the gap between the bounds converges to zero as the stage aggregation is refined. If massive aggregation of stages is possible without sacrificing too much accuracy, the aggregate approximate problems can be addressed by means of scenario tree-based methods. The suggested approach applies to problems that exhibit randomness in the objective and the constraints, while the constraint functions are required to be additively separable in the decision variables and random parameters.
PB - INFORMS
CY - Hanover, USA
SN - 0364-765X
JF - Mathematics of Operations Research
VL - 2
IS - 34
SP - 428
EP - 444
ER -
TY - JOUR
TI - Convergent Bounds for Stochastic Programs with Expected Value Constraints
AU - Kuhn, D.
PY - 2009
N2 - This article describes a bounding approximation scheme for convex multistage stochastic programs (MSP) that constrain the conditional expectation of some decision-dependent random variables. Expected value constraints of this type are useful for modelling a decision maker’s risk preferences, but they may also arise as artifacts of stage-aggregation. We develop two finite-dimensional approximate problems that provide bounds on the (infinite-dimensional) original problem, and we show that the gap between the bounds can be made smaller than any prescribed tolerance. Moreover, the solutions of the approximate MSPs give rise to a feasible policy for the original MSP, and this policy’s optimality gap is shown to be smaller than the difference of the bounds. The considered problem class comprises models with integrated chance constraints and conditional value-at-risk constraints. No relatively complete recourse is assumed.
PB - Springer Netherlands
SN - 0022-3239
JF - Journal of Optimization Theory and Applications
VL - 3
IS - 141
SP - 597
EP - 618
ER -
TY - JOUR
TI - Dynamic Mean-Variance Portfolio Analysis under Model Risk
AU - Kuhn, D.
AU - Parpas, P.
AU - Rustem, B.
AU - Fonseca, R.
PY - 2009
N2 - The classical Markowitz approach to portfolio selection is compromised by two major shortcomings. First, there is considerable model risk with respect to the distribution of asset returns. Particularly, mean returns are notoriously difficult to estimate. Moreover, the Markowitz approach is static in that it does not account for the possibility of portfolio rebalancing within the investment horizon. We propose a robust dynamic portfolio optimization model to overcome both shortcomings. The model arises from an infinite-dimensional min-max framework. The objective is to minimize the worst-case portfolio variance over a family of dynamic investment strategies subject to a return target constraint. The worst-case variance is evaluated with respect to a set of conceivable return distributions. We develop a quantitative approach to approximate this intractable problem by a tractable one and report on numerical experiments.
PB - Risk Journals, Incisive Media
CY - London
SN - 1460-1559
JF - Journal of Computational Finance
VL - 12 (4)
SP - 91
EP - 115
ER -
TY - JOUR
TI - Valuation of electricity swing options by multistage stochastic programming
UR - https://www.alexandria.unisg.ch/publications/52991
AU - Kuhn, D.
AU - Haarbrücker, G.
PY - 2009
N2 - Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation of decision stages, discretization of the probability space, and reparameterization of the decision space. We report on numerical results and discuss analytically tractable limiting cases.
PB - Elsevier
SN - 0005-1098
JF - Automatica
VL - 45 (4)
SP - 889
EP - 899
ER -
TY - CHAP
TI - Stochastic optimization of investment planning problems in the electric power industry
T2 - Energy Systems Engineering
AU - Kuhn, D.
AU - Parpas, P.
AU - Rustem, B.
PY - 2008
T3 - Process Systems Engineering
PB - Wiley-VCH
CY - Weinheim
SN - 978-3-527-31694-6
SP - 215
EP - 230
ER -
TY - CHAP
TI - Threshold Accepting Approach to Improve Bound-based Approximations for Portfolio Optimization
T2 - Computational Methods in Financial Engineering
AU - Kuhn, D.
AU - Parpas, P.
AU - Rustem, B.
PY - 2008
N2 - A discretization scheme for a portfolio selection problem is discussed. The model is a benchmark relative, mean-variance optimization problem in continuous time. In order to make the model computationally tractable, it is discretized in time and space. This approximation scheme is designed in such a way that the optimal values of the approximate problems yield bounds on the optimal value of the original problem. The convergence of the bounds is discussed as the granularity of the discretization is increased. A threshold accepting algorithm that attempts to find the most accurate discretization among all discretizations of a given complexity is also proposed. Promising results of a numerical case study are provided.
PB - Springer
CY - Berlin, Heidelberg
SN - 978-3-540-77957-5
SP - 3
EP - 26
ER -
TY - JOUR
TI - Aggregation and discretization in multistage stochastic programming
AU - Kuhn, D.
PY - 2008
N2 - Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.
PB - Springer
CY - Berlin / Heidelberg
SN - 0025-5610
JF - Mathematical Programming, Series A
VL - 113 (1)
SP - 61
EP - 94
ER -
TY - JOUR
TI - Bound-Based Decision Rules in Multistage Stochastic Programming
AU - Kuhn, D.
AU - Parpas, P.
AU - Rustem, B.
PY - 2008
N2 - We study bounding approximations for a multistage stochastic program with expected value constraints. Two simpler approximate stochastic programs, which provide upper and lower bounds on the original problem, are obtained by replacing the original stochastic data process by finitely supported approximate processes. We model the original and approximate processes as dependent random vectors on a joint probability space. This probabilistic coupling allows us to transform the optimal solution of the upper bounding problem to a near-optimal decision rule for the original problem. Unlike the scenario tree based solutions of the bounding problems, the resulting decision rule is implementable in all decision stages, i. e., there is no need for dynamic reoptimization during the planning period. Our approach is illustrated with a mean-risk portfolio optimization model.
PB - Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic
CY - Prague
SN - 0023-5954
JF - Kybernetika
VL - 44(2)
SP - 34
EP - 150
ER -
TY - UNPB
TI - Dynamic Mean-Variance Portfolio Analysis under Model Risk
AU - Kuhn, D.
AU - Parpas, P.
AU - Rustem, B.
PY - 2007
ER -
TY - UNPB
TI - An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time
AU - Kuhn, D.
PY - 2007
ER -
TY - UNPB
TI - BIT@EPI.VPP: A Software Package for the Valuation of Energy Contracts - Mathematical Documentation
AU - Bloechlinger, L.
AU - Haarbrücker, G.
AU - Kuhn, D.
PY - 2007
ER -
TY - UNPB
TI - BIT@EPI.HYDRO: A Software Tool for the Optimization of Hydro Power Plants
AU - Bloechlinger, L.
AU - Haarbrücker, G.
AU - Kuhn, D.
PY - 2007
ER -
TY - UNPB
TI - Analysis of the Rebalancing Frequency in Log-Optimal Portfolio Selection
AU - Kuhn, D.
AU - Luenberger, D. G.
PY - 2006
N2 - In a dynamic investment situation, the right timing of portfolio revisions and adjustments is essential to sustain long-term growth. A high rebalancing frequency reduces the portfolio performance in the presence of transaction costs, whereas a low rebalancing frequency entails a static investment strategy that hardly reacts to changing market conditions. This article studies a family of portfolio problems which depend parametrically on the rebalancing frequency. As an objective criterion we use log-utility, which has strong theoretical appeal and represents a natural choice if the primary goal is long-term performance. We show that continuous rebalancing only slightly outperforms discrete rebalancing if there are no transaction costs and if the rebalancing intervals are shorter than about one year. This result suggests that finite transaction costs are of minor concern since their effect on infrequently rebalanced portfolios is negligible.
ER -
TY - JOUR
TI - Convergent Bounds for Stochastic Programs with Expected Value Constraints
AU - Kuhn, D.
PY - 2006
N2 - This article elaborates a bounding approximation scheme for convex multistage stochastic programs (MSP) that constrain the conditional expectation of some decision-dependent random variables. Expected value constraints of this type are useful for modelling a decision maker's risk preferences, but they may also arise as artefacts of stage-aggregation. It is shown that the gap between certain upper and lower bounds on the optimal objective value can be made smaller than any prescribed tolerance. Moreover, the solutions of some tractable approximate MSP give rise to a policy which is feasible in the (untractable) original MSP, and this policy's cost differs from the optimal cost at most by the difference between the bounds. The considered problem class comprises models with integrated chance constraints and conditional value-at-risk constraints. No relatively complete recourse is assumed.
JF - The Stochastic Programming E-Print Series (SPEPS)
VL - 22
SP - 34
ER -
TY - JOUR
TI - Aggregation and Discretization in Multistage Stochastic Programming
AU - Kuhn, D.
PY - 2006
N2 - Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.
PB - Springer-Verlag
SN - 0025-5610
JF - Mathematical Programming, Series A (Forthcoming)
SP - 34
ER -
TY - UNPB
TI - Valuation of Electricity Swing Options by Multistage Stochastic Programming
UR - https://www.alexandria.unisg.ch/publications/29493
AU - Haarbrücker, G.
AU - Kuhn, D.
PY - 2006
N2 - Electricity swing options are American-style path-dependent power derivatives. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation of decision stages, discretization of the probability space, and reparameterization of the decision space. We report on insightful numerical results and discuss analytically tractable limiting cases.
ER -
TY - JOUR
TI - Swing-Optionen im Elektrizitätsmarkt - Bewertung und optimale Ausübung komplexer Stromderivate
UR - https://www.alexandria.unisg.ch/publications/19888
AU - Frauendorfer, K.
AU - Haarbrücker, G.
AU - Kuhn, D.
AU - Kiske, K.
PY - 2005
N2 - Die im Elektrizitätsmarkt als Swing-Optionen bekannten Derivate sind hinsichtlich ihres Charakters und ihrer Einsatzgebiete klassischen Call- und Put-Optionen aus der Finanzwelt ähnlich. So geben Swing-Optionen dem Optionshalter das Recht, während der vereinbarten Ausübungsperiode Energie zu einem vertraglich festgelegten Preis zu kaufen (Call) oder zu verkaufen (Put). Analog den klassischen Finanzoptionen eignen sich Swing-Optionen daher einerseits als Absicherungsinstrumente, andererseits lassen sich spekulative Interessen verfolgen. Die Bewertung von Swing-Optionen erweist sich jedoch als ungleich schwerer, denn oft ist eine solche Option nicht nur durch Rechte, sondern auch durch Verpflichtungen gekennzeichnet. Der hohen Komplexität dieser Derivate kann man mit numerischen Bewertungsmethoden begegnen.
PB - Energieportal GmbH & Co. KG
CY - Essen
SN - 1611-2997
JF - e|m|w Zeitschrift für Energie, Markt, Wettbewerb
VL - 0
IS - 5
SP - 70
EP - 74
ER -
TY - JOUR
TI - Stochastische Optimierung im Energiehandel: Entscheidungsunterstützung und Bewertung für das Portfoliomanagement
UR - https://www.alexandria.unisg.ch/publications/7061
AU - Frauendorfer, K.
AU - Güssow, J.
AU - Haarbrücker, G.
AU - Kuhn, D.
PY - 2005
N2 - 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.
PB - Energieportal GmbH & Co. KG
CY - Essen, DE
SN - 1611-2997
JF - e|m|w Zeitschrift für Energie, Markt, Wettbewerb
VL - 0
IS - 1
SP - 59
EP - 66
ER -
TY - BOOK
TI - Generalized Bounds for Convex Multistage Stochastic Programs
AU - Kuhn, D.
PY - 2005
N2 - This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or their extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A distinct primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. Exemplary applications are studied to assess the performance of the theoretical concepts in situations of practical relevance. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can typically be reduced to a few percent at reasonable problem dimensions.
T3 - Lecture Notes in Economics and Mathematical Systems
PB - Springer-Verlag
CY - Berlin, DE
SN - 3-540-22540-4
SP - 190
ER -
TY - JOUR
TI - Supercurrents Through Gated Superconductor-Normal-Metal-Superconductor Contacts: the Josephson Transistor
AU - Kuhn, D.
AU - Chtchelkatchev, N. M.
AU - Lesovik, G. B.
AU - Blatter, G.
PY - 2001
N2 - We analyze the transport through a narrow ballistic superconductor-normal-metal–superconductor Josephson contact with non-ideal transmission at the superconductor–normal-metal interfaces, e.g., due to insulating layers, effective mass steps, or band misfits (SIN interfaces). The electronic spectrum in the normal wire is determined through the combination of Andreev- and normal reflection at the SIN interfaces. Strong normal scattering at the SIN interfaces introduces electron- and hole-like resonances in the normal region which show up in the quasi-particle spectrum. These resonances have strong implications for the critical supercurrent I_c which we find to be determined by the lowest quasi-particle level: tuning the potential µ_{x0} to the points where electron- and hole-like resonances cross, we find sharp peaks in I_c, resulting in a transitor effect. We compare the performance of this Resonant Josephson-Transistor (RJT) with that of a Superconducting Single Electron Transistor (SSET).
JF - Physical Review B
VL - 5
IS - 63
SP - 0545200
ER -