Scenario generation with distribution functions and correlations

Kaut, Michal; Lium, Arnt-Gunnar

doi:10.14736/kyb-2014-6-1049

Cited by 2 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The aim is to construct sets of scenarios with prescribed statistical properties, such as moments of the marginal distributions, correlations of the margins, percentiles of the marginal distributions etc. [61]. It is a generalization of the momentmatching algorithms [14,47] and focuses on capturing the key statistical features instead of guaranteeing an exact representation of the distribution.…”

Section: Methodologiesmentioning

confidence: 99%

Problem-Driven Scenario Generation for Stochastic Programming Problems: A Survey

Chou,

Messina

2023

Algorithms

View full text Add to dashboard Cite

Stochastic Programming is a powerful framework that addresses decision-making under uncertainties, which is a frequent occurrence in real-world problems. To effectively solve Stochastic Programming problems, scenario generation is one of the common practices that organizes realizations of stochastic processes with finite discrete distributions, which enables the use of mathematical programming models of the original problem. The quality of solutions is significantly influenced by the scenarios employed, necessitating a delicate balance between incorporating informative scenarios and preventing overfitting. Distributions-based scenario generation methodologies have been extensively studied over time, while a relatively recent concept of problem-driven scenario generation has emerged, aiming to incorporate the underlying problem’s structure during the scenario generation process. This survey explores recent literature on problem-driven scenario generation algorithms and methodologies. The investigation aims to identify circumstances under which this approach is effective and efficient. The work provides a comprehensive categorization of existing literature, supplemented by illustrative examples. Additionally, the survey examines potential applications and discusses avenues for its integration with machine learning technologies. By shedding light on the effectiveness of problem-driven scenario generation and its potential for synergistic integration with machine learning, this survey contributes to enhanced decision-making strategies in the context of uncertainties.

show abstract

Section: Methodologiesmentioning

confidence: 99%

Problem-Driven Scenario Generation for Stochastic Programming Problems: A Survey

Chou,

Messina

2023

Algorithms

View full text Add to dashboard Cite

show abstract

“…It is noted that a copula is a continuous function by its definition. The well-known result due to Sklar (1973), who employed the term "copula" almost for the first time, gives a fundamental property of copulas. We recall here Sklar's theorem in bivariate case, for completeness of our presentation.…”

Section: Copulamentioning

confidence: 99%

Remarks on a copula‐based conditional value at risk for the portfolio problem

Molina Barreto,

Ishimura

2023

Intell Sys Acc Fin Mgmt

View full text Add to dashboard Cite

SummaryWe deal with a multivariate conditional value at risk. Compared with the usual notion for the single random variable, a multivariate value at risk is concerned with several variables, and thus, the relation between each risk factor should be considered. We here introduce a new definition of copula‐based conditional value at risk, which is real valued and ready to be computed. Copulas are known to provide a flexible method for handling a possible nonlinear structure; therefore, copulas may be naturally involved in the theory of value at risk. We derive a formula of our copula‐based conditional value at risk in the case of Archimedean copulas, whose effectiveness is shown by examples. Numerical studies are also carried out with real data, which can be verified with analytical results.

show abstract

Scenario generation with distribution functions and correlations

Cited by 2 publications

References 25 publications

Problem-Driven Scenario Generation for Stochastic Programming Problems: A Survey

Problem-Driven Scenario Generation for Stochastic Programming Problems: A Survey

Remarks on a copula‐based conditional value at risk for the portfolio problem

Contact Info

Product

Resources

About