Distributionally robust inference for extreme Value-at-Risk

Yuen, Robert; Stoev, Stilian; Cooley, Daniel

doi:10.1016/j.insmatheco.2020.03.003

Cited by 7 publications

(1 citation statement)

References 25 publications

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“…Moreover, the safety operation of the distribution system needs to handle the risk of changes in system supply and demand, when the uncertain power of WTs/PVs is injected into the distribution system. Financial institutions use value-at-risk (VAR) to evaluate risk in uncertainty, by measuring the minimum loss expected in Energies 2020, 13, 5852 2 of 16 a given portfolio within an assigned period [6,7]. It is important to carry out risk assessment and seek the optimal operation in the case of uncertain power supply.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Phase Arrangement of Distribution Transformers under Risk Assessment

Yang

Tsai

2020

Energies

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This paper presents a phase arrangement procedure for distribution transformers to improve system unbalance and voltage profile of distribution systems, while considering the location and uncertainties of the wind turbine (WT) and photovoltaics (PV). Based on historical data, the Monte Carlo method is used to calculate the power generation value-at-risk (VAR) of WTs/PVs installed under a given level of confidence. The main target of this paper is to reduce the line loss and unbalance factor during 24-hour intervals. Assessing the various confidence levels of risk, a feasible particle swarm optimization (FPSO) is proposed to solve the optimal location of WTs/PVs installed and transformer load arrangement. A three-phase power flow with equivalent current injection (ECI) is analyzed to demonstrate the operating efficiency of the FPSO in a Taipower feeder. Simulation results will support the planner in the proper location of WTs/PVs installed to reduce system losses and maintain the voltage profile. They can also provide more risk information for handing uncertainties when the renewable energy is connected to the distribution system.

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Section: Introductionmentioning

confidence: 99%

An Optimal Phase Arrangement of Distribution Transformers under Risk Assessment

Yang

Tsai

2020

Energies

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Tail-dependence, exceedance sets, and metric embeddings

2023

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There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the matrix of bivariate tail-dependence coefficients. This paper starts by providing a review of existing results from a unifying perspective, which highlights connections between extreme value theory and the theory of cuts and metrics. Our approach leads to some new findings in both areas with some applications to current topics in risk management.We begin by using the framework of multivariate regular variation to show that extremal coefficients, or equivalently, the higher-order tail-dependence coefficients of a random vector can simply be understood in terms of random exceedance sets, which allows us to extend the notion of Bernoulli compatibility. In the special but important case of bivariate tail-dependence, we establish a correspondence between tail-dependence matrices and $$L^1$$ L 1 - and $$\ell _1$$ ℓ 1 -embeddable finite metric spaces via the spectral distance, which is a metric on the space of jointly 1-Fréchet random variables. Namely, the coefficients of the cut-decomposition of the spectral distance and of the Tawn-Molchanov max-stable model realizing the corresponding bivariate extremal dependence coincide. We show that line metrics are rigid and if the spectral distance corresponds to a line metric, the higher order tail-dependence is determined by the bivariate tail-dependence matrix.Finally, the correspondence between $$\ell _1$$ ℓ 1 -embeddable metric spaces and tail-dependence matrices allows us to revisit the realizability problem, i.e. checking whether a given matrix is a valid tail-dependence matrix. We confirm a conjecture of Shyamalkumar and Tao (2020) that this problem is NP-complete.

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Stochastic ordering in multivariate extremes

Corradini,

Strokorb

2024

Extremes

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The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension $$d\ge 3$$ d ≥ 3 these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiß family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiß family this holds true even for the supermodular order.

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Distributionally robust inference for extreme Value-at-Risk

Cited by 7 publications

References 25 publications

An Optimal Phase Arrangement of Distribution Transformers under Risk Assessment

An Optimal Phase Arrangement of Distribution Transformers under Risk Assessment

Tail-dependence, exceedance sets, and metric embeddings

Stochastic ordering in multivariate extremes

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