  Financial portfolios are often optimized for maximum profit while subject to
a constraint formulated in terms of the Conditional Value-at-Risk (CVaR). This
amounts to solving a linear problem. However, in its original formulation this
linear problem has a very large number of linear constraints, too many to be
enforced in practice. In the literature this is addressed by a reformulation of
the problem using so-called dummy variables. This reduces the large number of
constraints in the original linear problem at the cost of increasing the number
of variables. In the context of reinsurance portfolio optimization we observe
that the increase in variable count can lead to situations where solving the
reformulated problem takes a long time. Therefore we suggest a different
approach. We solve the original linear problem with cutting-plane method: The
proposed algorithm starts with the solution of a relaxed problem and then
iteratively adds cuts until the solution is approximated within a preset
threshold. This is a new approach. For a reinsurance case study we show that a
significant reduction of necessary computer resources can be achieved.
