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 problem has a very large number of constraints, too many to be enforced in practice. In the literature this is addressed by a reformulation of the problem using so-called auxiliary 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. The application of this method to financial portfolios is not documented in the literature at this point in time. For a reinsurance case study we show that a significant reduction of necessary computer resources can be achieved.
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