It is widely accepted to use conditional value-at-risk for risk management needs and option pricing. As a rule, there are difficulties in exact calculations of value-at-risk. In the paper, we methodology price spread options, extending some approximation approaches these needs. Our results illustrate by numerical which demonstrate their effectiveness. We also show how pricing can help with regu...

This paper presents a self-scheduling framework, using risk-constrained optimization model for the home energy management system (HEMS), considering fixed, controllable, and interruptible loads, as new contribution to earlier studies. The objectives are reducing electricity bill managing risk of purchasing over on-peak hours prosumer's discomfort index (DI) due shifting load undesired hours. In...

Abstract This paper focuses on a class of variational inequalities (VIs), where the map defining VI is given by component-wise conditional value-at-risk (CVaR) random function. We focus solving using sample average approximation, solutions are estimated with that uses empirical estimates CVaRs. establish two properties for this scheme. First, under continuity and uncertainty taking values in bo...

Suppose that N is a Z+-valued random variable and that X,X1, X2, . . . is a sequence of independent and identically distributed Z+ random variables independent of N . In this paper we are interested in properties of the conditional variable Nk D =(N | ∑Nj=1 Xj = k). In particular, we want to know the asymptotic behavior of the conditional mean ENk or the conditional variance var Nk as k → ∞. We...