A sequential elimination approach to value-at-risk and conditional value-at-risk selection

Conditional Value-at-Risk (CVaR) is a widely used metric of risk in portfolio analysis, interpreted as the expected loss when the loss is larger than a threshold defined by a quantile. This work is motivated by situations where the CVaR is given, and the objective is to find the portfolio with the largest or smallest quantile that meets the CVaR constraint. We define our problem within the classic stochastic multi-armed bandit (MAB) framework, and present two algorithms. One that can be used to find the portfolio with largest or smallest loss threshold that satisfies the CVaR constraint with high probability, and another that determines the portfolio with largest or smallest probability of exceeding a loss threshold implied by a CVaR constraint, also at some desired probability level.