In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds. Keywords Stochastic programming • Mean-risk models • Conditional value-at-risk • Mixed-integer recourse • Convex approximations Mathematics Subject Classification 90C11 • 90C15 • 90C59 Maarten H. van der Vlerk was actively involved in an early stage of this research, but passed away during the writing of this paper.

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