Shortfall Risk Models When Information on Loss Function Is Incomplete

Utility-based shortfall risk measures effectively captures a decision maker's risk attitude on tail losses. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of shortfall risk, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of plausible utility-based shortfall risk measures and define a so-called preference robust shortfall risk as through the worst risk that can be measured in this (ambiguity) set. We then apply the robust shortfall risk paradigm to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programs when the underlying exogenous uncertainty is discretely distributed.

Clarifying the Interpretation and Use of the LOLE Resource Adequacy Metric

The loss-of-load expectation (LOLE) risk metric has been used in probabilistic power system resource adequacy assessment for over 70 years, and today is one of the most recognizable and widely-used measures of system shortfall risk. However, this wide adoption has been accompanied by ambiguities and inconsistencies in its definition and application. This paper provides a unifying reference for defining the metric as it relates to modern analyses, while clarifying a number of common points of confusion in its application. In particular, the paper clarifies that LOLE is not a measure of expected total shortfall duration, a 2.4 hours per year LOLE target implies a less reliable system than a 1 day in 10 years (0.1 days per year) LOLE target, and exact conversions between hourly and daily LOLE targets are not generally possible. Illustrative examples are provided to help explain each of these points.

Clarifying the Interpretation and Use of the LOLE Resource Adequacy Metric

The loss-of-load expectation (LOLE) risk metric has been used in probabilistic power system resource adequacy assessment for over 70 years, and today is one of the most recognizable and widely-used measures of system shortfall risk. However, this wide adoption has been accompanied by ambiguities and inconsistencies in its definition and application. This paper provides a unifying reference for defining the metric as it relates to modern analyses, while clarifying a number of common points of confusion in its application. In particular, the paper clarifies that LOLE is not a measure of expected total shortfall duration, a 2.4 hours per year LOLE target implies a less reliable system than a 1 day in 10 years (0.1 days per year) LOLE target, and exact conversions between hourly and daily LOLE targets are not generally possible. Illustrative examples are provided to help explain each of these points.