We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating...

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the...