Scenario tree generation for multiperiod financial optimization by optimal discretization

By Georg Ch. Pflug. Mathematical programming, 2001

391 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ae6c6e7ba6a5b8cf7d3c555a5eb811704491c46f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Economics and Econometrics

In Management Science and Operations Research

Citations in the corpus

Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network (2013, methodology): “General scenario clustering techniques have been used previously in the stochastic optimization literature by Pflug (2001) and Latorre et al. (2007).”
Scenario Reduction for Futures Market Trading in Electricity Markets (2009, methodology): “Reference [15] describes an optimal discretization method that seeks to find an approximation of the initial scenario set that minimizes an error based on the objective function.”
Scenario reduction in stochastic programming (2003, methodology): “The author of [ 14 ] develops a deterministic iteration scheme in case P is completely known and a stochastic approximation method based on empirical approximations of P . So far numerical experience is available for low dimensional test problems.”
A Stochastic Programming Approach to Electric Energy Procurement for Large Consumers (2007, background): “this gives the Wasserstein metric of order , that can be shown to have some appealing properties when approximating stochastic optimization problems [17].”
Optimization of Electricity Retailer's Contract Portfolio Subject to Risk Preferences (2010, background): “line of research in scenario generation techniques [22]–[27],”
Generation of multivariate scenario trees to model stochasticity in power management (2005, neutral): “We mention here in chronological order (i) bound-based approximationmethods [11], [8], [4], (ii) Monte Carlo-basedsampling schemes [21], [5], [2], [31], (iii) the moment-matching principle[19], [20], (iv) optimalapproximations based on probability metrics[25], [18], [7], [13], and (v) the use…”
Monte Carlo sampling-based methods for stochastic optimization (2014, neutral): “A review of this technique can be found in Ermoliev [75]; discussion on practical aspects such as choice of stepsizes, stopping rules and implementation guidelines are given by Gaivoronski [84] and Pflug [189].”
Scenario tree modeling for multistage stochastic programs (2009, methodology): “We mention here (i) bound-based constructions [1, 8], (ii) Monte Carlo-based schemes [2, 33, 34] or Quasi Monte Carlo-based methods [22, 21], (iii) EVPI-based sampling and reduction within decomposition schemes [3], (iv) the moment-matching principle [17, 18], (v) probability metric based approximat”
Approximations for Probability Distributions and Stochastic Optimization Problems (2011, methodology): “For a proof see Pflug (2009).”
Forward Contracting and Selling Price Determination for a Retailer (2007, neutral): “, time-series models [27], momentmatching [28] and [29], clustering [30] and [31], etc.”
Scenario reduction in stochastic programming: An approach using probability metrics (2000, methodology): “attempt for solving (8) is made in [14] in case of c = c1 and = R , where the scenarios {ωj : j = 1, .”
A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty (2003, background): “It is worthwhile to mention that, although in principle, scenario trees can be used to represent a wide variety of distributions and correlations; in practice, accurate approximation of a complex stochastic process by a modest-sized scenario tree is a very difficult problem in approximation theory [”
Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation (2002, background): “{Institute of Mathematics, Humboldt University Berlin, Berlin, Germany.”