Equivalence of the problems with quantile and integral quantile criteria

Consideration was given to the relation between the problems of stochastic programming with criteria in the form of quantile (VaR) and integral quantile (CVaR). Conditions were established for coincidence and distinction between their solutions. Different cases of the loss function and the distribution function of a random vector were discussed. In particular, the problem with bilinear loss function was explored to which the problem of generating the investment portfolio comes.