Tree approximation for discrete time stochastic processes: a process distance approach

Kovacevic, Raimund M.; Pichler, Alois

doi:10.1007/s10479-015-1994-2

Cited by 30 publications

(20 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Efficient techniques also employ stochastic approximation. Kovacevic and Pichler (2015) generalize the techniques to stochastic processes, whilst Pflug and Pichler (2016) also propose probabilistic approaches.…”

Section: Distretization Of (Drro) Through Empirical Probability Distrmentioning

confidence: 99%

Quantitative stability analysis for minimax distributionally robust risk optimization

Pichler

2018

Math. Program.

Self Cite

View full text Add to dashboard Cite

This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage. We carry out a stability analysis by looking into variations of the ambiguity set under the Wasserstein metric, decision spaces at both stages and the support set of the random variables. In the case when the risk measure is risk neutral, the stability result is presented with the variation of the ambiguity set being measured by generic metrics of ζ-structure, which provides a unified framework for quantitative stability analysis under various metrics including total variation metric and Kantorovich metric. When the ambiguity set is structured by a ζ-ball, we find that the Hausdorff distance between two ζ-balls is bounded by the distance of their centers and difference of their radii. The findings allow us to strengthen some recent convergence results on distributionally robust optimization where the center of the Wasserstein ball is constructed by the empirical probability distribution.

show abstract

Section: Distretization Of (Drro) Through Empirical Probability Distrmentioning

confidence: 99%

Quantitative stability analysis for minimax distributionally robust risk optimization

Pichler

2018

Math. Program.

Self Cite

View full text Add to dashboard Cite

show abstract

“…i.e., an infinite sum of the product of a Poisson distribution with parameter λ(t 2 − t 1 ), a Binomial distribution with probability parameter t/(t 2 − t 1 ), and a complicated multidimensional integral over the conditional densities (using a shorthand notation) given in (23).…”

Section: Proof Using the Convolution Properties Of The Exponential DImentioning

confidence: 99%

“…Therefore, one often reverts to scenario lattices in such cases. While the literature on the construction of scenario trees is relatively rich (see, e.g., [16,18,23,32,33]), the lattice construction literature is rather sparse. The state-of-the art approach is based on the minimization of a distance measure between the targeted distribution and its discretization ("optimal quantization"), see [3,25,32].…”

Section: Introductionmentioning

confidence: 99%

Multiscale stochastic optimization: modeling aspects and scenario generation

Glanzer

Pflug

2019

Comput Optim Appl

View full text Add to dashboard Cite

Real-world multistage stochastic optimization problems are often characterized by the fact that the decision maker may take actions only at specific points in time, even if relevant data can be observed much more frequently. In such a case there are not only multiple decision stages present but also several observation periods between consecutive decisions, where profits/costs occur contingent on the stochastic evolution of some uncertainty factors. We refer to such multistage decision problems with encapsulated multiperiod random costs, as multiscale stochastic optimization problems. In this article, we present a tailor-made modeling framework for such problems, which allows for a computational solution. We first establish new results related to the generation of scenario lattices and then incorporate the multiscale feature by leveraging the theory of stochastic bridge processes. All necessary ingredients to our proposed modeling framework are elaborated explicitly for various popular examples, including both diffusion and jump models. Keywords Stochastic programming • Scenario generation • Bridge process • Stochastic bridge • Diffusion bridge • Lévy bridge • Compound Poisson bridge • Simulation of stochastic bridge • Multiple time scales • Multi-horizon • Multistage stochastic optimization

show abstract

“…In order to mitigate the effect that only "smaller" trees can be handled, methods for constructing representative but small scenario trees have therefore received significant attention. Let us mention the pioneering work [13] on two-stage programs and some subsequent extensions to the multistage case: e.g., [14][15][16][17][18]. Other ideas to reduce the computational burden rely on combining adaptive partitioning of scenarios with regularization techniques from convex optimization, e.g., [19,20].…”

Section: Introductionmentioning

confidence: 99%

On conditional cuts for stochastic dual dynamic programming

Ackooij¹,

Warin²

2020

EURO Journal on Computational Optimization

View full text Add to dashboard Cite

Multi stage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management. A popular method is Stochastic Dual Dynamic Programming (SDDP), especially when the dimensionality of the problem is large and Dynamic programming no longer an option. The usual assumption of SDDP is that uncertainty is stage-wise independent, which is highly restrictive from a practical viewpoint. When possible, the usual remedy is to increase the statespace to account for some degree of dependency. In applications this may not be possible or it may increase the state space by too much. In this paper we present an alternative based on keeping a functional dependency in the SDDP -cuts related to the conditional expectations in the dynamic programming equations. Our method is based on popular methodology in mathematical finance, where it has progressively replaced scenario trees due to superior numerical performance. On a set of numerical examples, we too show the interest of this way of handling dependency in uncertainty, when combined with SDDP. Our method is readily available in the open source software package StOpt.

show abstract

Tree approximation for discrete time stochastic processes: a process distance approach

Cited by 30 publications

References 27 publications

Quantitative stability analysis for minimax distributionally robust risk optimization

Quantitative stability analysis for minimax distributionally robust risk optimization

Multiscale stochastic optimization: modeling aspects and scenario generation

On conditional cuts for stochastic dual dynamic programming

Contact Info

Product

Resources

About