Scenario tree generation approaches using K-means and LP moment matching methods

Xu, Donghai; Chen, Zhiping; Yang, Li

doi:10.1016/j.cam.2012.05.020

Cited by 65 publications

(58 citation statements)

References 18 publications

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“…To ensure its implementability and overall efficiency, the hybrid method we proposed in Xu et al (2012) is adopted here to describe the parametric model and to generate necessary scenarios in the following experiments. The hybrid method combines the Kmeans clustering technique and the LP moment matching skill to generate a scenario tree, one can refer to Xu et al (2012) for details.…”

Section: Multi-period Portfolio Selection Modelmentioning

confidence: 99%

Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Chen

Liu

et al. 2015

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Through the composition of two real-valued functions, we propose a new class of multi-period risk measure which is time consistent. The new multi-period risk measure is monotonous and convex when the two real-valued functions satisfy monotonicity and convexity. Based on this generic framework, we construct a specific class of time-consistent multi-period risk measure by considering the lower partial moment between the realized wealth and the target wealth at individual periods. With the new multi-period risk measure as the objective function, we formulate a multi-period portfolio selection model by considering transaction costs at individual investment periods. Furthermore, this stochastic programming model is transformed into a deterministic programming problem using the scenario tree technology. Finally, we show through empirical tests and comparisons the rationality, practicality and efficiency of our new multi-period risk measure and the corresponding portfolio selection model.

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Section: Multi-period Portfolio Selection Modelmentioning

confidence: 99%

Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Chen

Liu

et al. 2015

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“…In particular, some authors have used variants of the k-means clustering algorithm, where the main goal is to group or aggregate paths in the scenario tree that are "near" to each other according to some distance metric that is minimized. For instance, Xu, Chen, & Yang (2012) proposed a k-means algorithm that generates a scenario tree from a fan-like tree that not only groups paths that are near in a probabilistic sense, but also accounts for inter-stage dependency of the data.…”

Section: Reducing the Scenario Treementioning

confidence: 99%

Data-driven multi-stage scenario tree generation via statistical property and distribution matching

Calfa

Agarwal

Grossmann

et al. 2014

Computers & Chemical Engineering

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The objective of this paper is to bring systematic methods for scenario tree generation to the attention of the Process Systems Engineering community. In this paper, we focus on a general, data-driven optimization-based method for generating scenario trees, which does not require strict assumptions on the probability distributions of the uncertain parameters. This method is based on the Moment Matching Problem (MMP), originally proposed by Høyland & Wallace (2001). In addition to matching moments, and in order to cope with potentially under-specified MMP, we propose matching (Empirical) Cumulative Distribution Function information of the uncertain parameters. The new method gives rise to a Distribution Matching Problem (DMP) that is aided by predictive analytics. We present two approaches for generating multi-stage scenario trees by considering time series modeling and forecasting. The aforementioned techniques are illustrated with a motivating production planning problem with uncertainty in production yield and correlated product demands.

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“…Inspired by that work, Xu et al (2012) design a new approach that combines simulation, the Kmeans clustering approach, and linear moment matching to generate the multi-stage scenario tree.…”

Section: Scenario Generationmentioning

confidence: 99%

“…This method matches the statistical properties of a geometric Brownian motion better than other algorithms in a situation when having as low a branching factor as possible is a priority. The algorithms described in Xu et al (2012) and Chen and Xu (2013) are definitely more efficient and can capture more complex models for asset returns, such as the vector autoregressive and multivariate generalized autoregressive conditional heteroscedasticity models, but they require a larger branching factor. For our choice of assets and the distribution parameters, the satisfactory statistical match is obtained for a branching factor of at least 8, whereas the algorithm presented in Høyland and Wallace (2001) allows to generate the required scenario tree with only 4 branches.…”

Section: Scenario Generationmentioning

confidence: 99%

A Combined Stochastic Programming and Optimal Control Approach to Personal Finance and Pensions

Konicz¹,

Pisinger

Rasmussen

et al. 2014

SSRN Journal

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Scenario tree generation approaches using K-means and LP moment matching methods

Cited by 65 publications

References 18 publications

Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Composite time-consistent multi-period risk measure and its application in optimal portfolio selection

Data-driven multi-stage scenario tree generation via statistical property and distribution matching

A Combined Stochastic Programming and Optimal Control Approach to Personal Finance and Pensions

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