Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double...

Growth of intermittent renewable energy and climate change make it increasingly difficult to manage electricity demand variability. Transmission and centralized storage technologies can help, but are costly. An alternative to centralized storage is to make better use of shiftable demand, but it...