Practical arbitrage‐free scenario tree reduction methods and their applications in financial optimization

Chen, Zhiping; Yan, Zhe

doi:10.1002/asmb.2290

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…Such methods are commonly used in decision‐making models that deal with uncertainty. The most common applications are found in portfolio and risk management for electrical power utilities 22,23 and in financial optimization 24,25 . In this framework, scenario reduction is used in the planning process to facilitate fast and still accurate optimization of the initial robust plan, as well as the adapted robust plans.…”

Section: Methodsmentioning

confidence: 99%

“…The most common applications are found in portfolio and risk management for electrical power utilities 22,23 and in financial optimization. 24,25 In this framework, scenario reduction is used in the planning process to facilitate fast and still accurate optimization of the initial robust plan, as well as the adapted robust plans. Here, we choose to apply the scenario-reduction and tree-generation algorithm proposed by Gr€ owe-Kuska et al, 23 which is wellsuited to handle the issue of intractability in robust planning for the following reasons.…”

Section: C Tractability and Scenario Reductionmentioning

confidence: 99%

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On adaptation cost and tractability in robust adaptive radiation therapy optimization

Böck

2020

Medical Physics

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Adaptation Cost and Tractability in Robust ARTPurpose: In this paper, a framework for online robust adaptive radiation therapy (ART) is discussed and evaluated. The purpose of the presented approach to ART is to: (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii) address adaptation cost and (iii) address computational tractability.Methods: A novel framework for online robust ART using the concept of Bayesian inference and scenario-reduction is introduced and evaluated in a series of treatment on a one-dimensional phantom geometry. The initial robust plan is generated from a robust optimization problem based on either expected-value-or worst-caseoptimization approach using the a priori hypothesis of the probability distribution governing the interfractional geometric variations. Throughout the course of every treatment, the simulated interfractional variations are evaluated in terms of their likelihood with respect to the a priori hypothesis of their distribution and violation of user-specified tolerance limits by the accumulated dose. If an adaptation is considered, the a posteriori distribution is computed from the actual variations using Bayesian inference. Then, the adapted plan is optimized to better suit the actual interfractional variations of the individual case. This adapted plan is used until the next adaptation is triggered. To address adaptation cost, the proposed framework provides an option for increased adaptation frequency. Computational tractability in robust planning and ART is addressed by approximation algorithms to reduce the size of the optimization problem.Results: According to the simulations, the proposed framework may improve target coverage compared to the corresponding non-adaptive robust approach. In particular, combining the worst-case-optimization approach with Bayesian inference may perform best in terms of improving CTV coverage and organ-at-risk (OAR) protection. Concerning adaptation cost, the results indicate that mathematical methods like Bayesian inference may have a greater impact on improving individual treatment quality than increased adaptation frequency. In addition, the simulations suggest that the concept of scenario-reduction may be useful to address computational tractability in ART and robust planning in general. Conclusion:The simulations indicate that the adapted plans may improve target coverage and OAR protection at manageable adaptation and computational cost

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Section: Methodsmentioning

confidence: 99%

Section: C Tractability and Scenario Reductionmentioning

confidence: 99%

On adaptation cost and tractability in robust adaptive radiation therapy optimization

Böck

2020

Medical Physics

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“…Both techniques use k-means approach as the core algorithm since it consists of a simple iterative process that accounts for the global distance to assign samples into k clusters (with k being user-defined) and then averages all the samples to create the new cluster centres (Hastie et al, 2008). Despite their use in a wide range of applications and proved computational benefits (Lima et al, 2018;Zeballos et al, 2018;Chen and Yan, 2018a;Medina-González et al, 2018a), the main limitation of SCENRED and OSCAR is their loss of accuracy and/or time effectiveness when the original set is significantly large (> 4, 000) or when the original dataset represents a low dimensional problem . Another important limitation of these methods is the lack of a rule/strategy to determine the reduced set size (i.e.…”

Section: Introductionmentioning

confidence: 99%

A graph theory approach for scenario aggregation for stochastic optimisation

Medina-González

Gkioulekas

Dua

et al. 2020

Computers & Chemical Engineering

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The development of fast, robust and reliable computational tools capable of addressing process management under uncertain conditions is an active topic in the current literature, and more precisely for the process systems engineering one. Particularly, scenario reduction strategies have emerged as an alternative to overcome the traditional issues associated with large-scale scenario-based problems. This work proposes a novel and flexible scenario-reduction alternative that integrates data mining, graph theory and community detection concepts to represent the uncertain information as a network and identify the most efficient communities/clusters. The capabilities of the proposed approach were tested by solving a set of two-stage mixed-integer linear programming problems under uncertainty. For comparison and validation purposes, these problems were also solved using the two available methods (SCENRED and OS-CAR). This comparison demonstrates the similar (and in some cases better) quality and accuracy of the proposed approach against the traditional methods. Additionally, the practical advantage of the proposed parameter definition rule is demonstrated as a way to overcome the limitations of the current alternatives (i.e. arbitrary user-defined parameters).

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Scenario reduction and scenario tree generation for stochastic programming using Sinkhorn distance

Kammammettu¹,

Li²

2023

Computers & Chemical Engineering

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Practical arbitrage‐free scenario tree reduction methods and their applications in financial optimization

Cited by 3 publications

References 33 publications

On adaptation cost and tractability in robust adaptive radiation therapy optimization

On adaptation cost and tractability in robust adaptive radiation therapy optimization

A graph theory approach for scenario aggregation for stochastic optimisation

Scenario reduction and scenario tree generation for stochastic programming using Sinkhorn distance

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