All rights resen ecl. No pa.rt of this publica ti o n m a.v be re pro duced o r tra ns mitted in a.ny form or by a n~' mea.ns. elec t ronic o r mec ha ni ca l. includin g photoco py, recordin g, or any inform a.t.ion s to rage o r retrie val syste m , \\·it ho ut pe rmissio n in writin g fr om t he co py right hold er. Abstract-This paper introduces an approach to modeling the uncertainties concerning future characteristics of energy technologies within the framework of long-term dynamic linear programming models. The approach chosen explicitly incorporates the uncertainties in the model, endogenizing interactions between decision structure and uncertainties involved. The use of this approach for future investment costs of electricity generation technologies in the framework of very long-term energy scenarios shows improvements in model behavior and more robust solutions with respect to technology choices made.

A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called CVaR (superquantile) regression. The main statement of this paper is: CVaR linear regression can be reduced to minimizing the Rockafellar error function with linear programming. The theoretical basis for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of CVaR quadrangle and mixed-quantile quadrangle for discrete distributions with equally probable atoms. The deviation in the CVaR quadrangle is an integral. We present two equivalent variants of discretization of this integral, which resulted in two sets of parameters for the mixed-quantile quadrangle. For the first set of parameters, the minimization of error from the CVaR quadrangle is equivalent to the minimization of the Rockafellar error from the mixed-quantile quadrangle. Alternatively, a two-stage procedure based on the decomposition theorem can be used for CVaR linear regression with both sets of parameters. This procedure is valid because the deviation in the mixed-quantile quadrangle (called mixed CVaR deviation) coincides with the deviation in the CVaR quadrangle for both sets of parameters. We illustrated theoretical results with a case study demonstrating the numerical efficiency of the suggested approach. The case study codes, data, and results are posted on the website. The case study was done with the Portfolio Safeguard (PSG) optimization package, which has precoded risk, deviation, and error functions for the considered quadrangles.

This paper develops trading strategies for liquidation of a financial security, which maximize the expected return. The problem is formulated as a stochastic programming problem that utilizes the scenario representation of possible returns. Two cases are considered, a case with no constraint on risk and a case when the risk of losses associated with trading strategy is constrained by Conditional Value-at-Risk (CVaR) measure. In the first case, two algorithms are proposed; one is based on linear programming techniques, and the other uses dynamic programming to solve the formulated stochastic program. The third proposed algorithm is obtained by adding the risk constraints to the linear program. The algorithms provide path-dependent strategies, i.e., the fraction of security sold depends upon price sample-path of the security up to the current moment. The performance of the considered approaches is tested using a set of historical sample-paths of prices.

The paper presents an algorithm to search for the lower bound of the Bayesian estimate of the parameter of exponential distribution in the case where it is known that a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in sensivity analysis of Bayesian estimates of failure rates to the choice of a priori distribution in the exponential failure model. INTRODUCTIONThe major accidents at the Three Mile Island in the USA and the Chernobyl Nuclear Power Plant have radically changed the approach to the safety of nuclear power plants. Before the accident at the Three Mile Island in 1979, the United States Atomic Energy Commission (now the Nuclear Regulatory Commission (NRC)) controlled nuclear plants based on the deterministic approach, which implied an analysis of standard operation modes and accidents, and assessed the efficiency of applying various protective measures. After this accident, the NRC has essentially changed the approach to the safety analysis of nuclear power plants and stimulated rapid development of probabilistic safety analysis (PSA) aimed not only at assessing the consequences of accidents, but also at assessing their probabilities.PSA has come to be regularly applied since the analysis of the molten core in 1975 [1]. The analysis revealed sequences of events that could cause significant radioactive releases and assessed the radiological consequences of these events and their probabilities. The results of this analysis underlied the decision made by the NRC to introduce PSA [2]. The PRA Procedures Guide [3] was published, which addressed various aspects of risk assessment and proposed methods for risk assessment at nuclear power plants. The methodology stated therein was widely used in safety analysis at nuclear power plants in the 1980s and 1990s. Many of its principles are still in force now.In 1988, the NRC required nuclear power plants to carry out probabilistic safety analysis. The results of the analysis at five nuclear power plants are summarized in NUREG-1150 [4]. This document develops the PSA methodology and indicates ways of using the results of safety analysis in the regulatory policy of the NRC. The PSA methodology outlined in NUREG-1150 is still of importance. It is intended to generate accident scenarios and to obtain quantitative risk estimates and allows identifying possible vulnerabilities of nuclear power plants. Since the results of safety analysis are used to license plants, one of the key requirements for PSA is to provide high accuracy.According to the IAEA Safety Guide [5], PSA is carried out at three levels. At the first level, sequences of events that may cause damage the core are analyzed, and the associated probability is assessed. At the second level, the possible paths of radioactive release outside the nuclear power plant are identified and their amount and frequency are assessed. At the third level, health effects of the accident and other public risks such as pollution of the territory or foodstuff ar...

We propose the use of regression models as a tool to reduce time and cost associated with the development and selection of new metallic alloys. A multiple regression model is developed which can accurately predict tensile yield strength of high strength low alloy steel based on its chemical composition and processing parameters. Quantile regression is used to model the fracture toughness response as measured by Charpy V-Notch (CVN) values, which exhibits substantial variability and is therefore not usefully modelled via standard regression with its focus on the mean. Using Monte-Carlo simulation, we determine that the three CVN values corresponding to each steel specimen can be plausibly modelled as observations from the 20th, 50th and 80th percentiles of the CVN distribution. Separate quantile regression models fitted at each of these percentile levels prove sufficiently accurate for ranking steels and selecting the best combinations of composition and processing parameters.