Application of Buffered Probability of Exceedance in Reliability Optimization Problems*

The paper proposes a new method of dynamic VaR and CVaR (ES) risk measures forecasting. Quantile linear GARCH model is chosen as the main forecasting model for time series quantiles. To build a forecast, the values of quantiles are approximated by the metalog distribution, which makes it possible to use analytical formulas to evaluate risk measures. The method of VaR and CVaR forecasting is formulated as a step-by-step algorithm. At the first stage, an initial model is built to obtain variance estimates. The predicted variance values obtained from the constructed model are used at the second stage to find the QLGARCH model coefficients by solving the minimization problem. At the third stage, the QLGARCH models are estimated on a non uniform quantile grid. The obtained predicted values of quantiles are used to estimate the approximating metalog distribution. The investigated theory is applied to VaR and CVaR forecasting for time series of daily log return of the DJI index.

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“… for VaR estimates: the Kupiec test (LRuc), Christoffersen's independence test (LRind), PoE statistics [17];…”

Section: Experiment Results and Discussionmentioning

confidence: 99%

Quintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution

Zrazhevsky

Zrazhevska

2021

SRIT

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“…В дефектоскопії та акустичному скануванні основною задачею є визначення фізичних та геометричних характеристик [4,6]. При керуванні динамічною поведінкою коливних та хвильових процесів в пружних тілах важливе значення має розрахунок відгуку з врахуванням наявності неоднорідностей з невідомими характеристиками [7]. Звичайно, це не є повний перелік практичних галузей, що потребують моделювання неоднорідностей в пружних тілах.…”

Section: вступunclassified

Modeling of Finite Inhomogeneities by Discret Singularities

Zrazhevsky

Zrazhevska

2021

JNAM

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This work focuses on development of a mathematical apparatus that allows to perform an approximate description of inhomogeneities of finite sizes in a continuous bodies by arranging the sources given on sets of smaller dimensions. The structure and properties of source densities determine the adequacy of the model. The theory of differential forms and generalized functions underlies this study. The boundary value problems with nonsmooth coefficients are formulated. The solutions of such problems is sought in the form of weakly convergent series and as an alternative - an equivalent recurrent set of boundary value problems with jumps. A feature of this approach is the ability to consistently improve the adequacy of the description of inhomogeneity. This is important because it allows to qualitatively assess the impact of real characteristic properties on the accuracy of the model description. Reducing the dimensions of inhomogeneities allows the use of efficient methods such as the Green's function and boundary integral equations to obtain a semi-analytic solution for direct and inverse problems. The work is based on a number of partial problems that demonstrate the proposed approach in modeling of inhomogeneities. The problems of modeling of the set of finite defects in an oscillating elastic beam, the set of inhomogeneities of an arbitrary shape in an oscillating plate, fragile cracks in a two-dimensional elastic body under static loading are considered.

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“…Buffered failure probabilities and the closely related buffered probabilities of exceedance [4] appear in several optimization models, often leveraging their connection with superquantiles (a.k.a. conditional/average value-atrisk), with applications in reliability engineering [10,1,21,2,3], data analytics [8], finance [16] and to address natural disasters [4]. However, gradient expressions for buffered failure probabilities as functions of parameters are not fully developed.…”

Section: Introductionmentioning

confidence: 99%

Gradients and Subgradients of Buffered Failure Probability

Røyset¹,

Byun²

2021

Preprint

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Gradients and subgradients are central to optimization and sensitivity analysis of buffered failure probabilities. We furnish a characterization of subgradients based on subdifferential calculus in the case of finite probability distributions and, under additional assumptions, also a gradient expression for general distributions. Several examples illustrate the application of the results, especially in the context of optimality conditions.

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Application of Buffered Probability of Exceedance in Reliability Optimization Problems*

Cited by 14 publications

References 8 publications

Quintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution

Quintile regression based approach for dynamical VaR and CVaR forecasting using metalog distribution

Modeling of Finite Inhomogeneities by Discret Singularities

Gradients and Subgradients of Buffered Failure Probability

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