A type or method of value at risk (VaR) that subjects the standard value at risk (for optimization of a portfolio/ a fund, etc.) to two constraints: a conditional value at risk or censored mean lower bound. The censored mean, for normal distributions (but not fat-tailed distributions), is equivalent to the statistical hazard function.

The censored mean for normal distributions would yield wider bounds for a given set of admissible portfolios, with a more complicated portfolio choice rule.