Translation-invariant and positive-homogeneous risk measures and optimal portfolio management in the presence of a riskless component

► Optimal portfolio is sought in the case of translation-invariant and positive homogeneous risk measure. ► The problem leads to the minimization of a combination of a linear and a square root of a quadratic functionals. ► Elliptical multivariate distribution is assumed. ► When the portfolio contains a riskless component the optimization becomes more complicated due to singularity of the covariance matrix. ► Explicit closed-form solution for this problem is provided.