Risk-Return Trade-off with the Scenario Approach in Practice: A Case Study in Portfolio Selection

We consider the scenario approach for chance constrained programming problems. Building on existing theoretical results, effective and readily applicable methodologies to achieve suitable risk-return trade-offs are developed in this paper. Unlike other approaches, that require solving non-convex optimization problems, our methodology consists of solving multiple convex optimization problems obtained by sampling and removing some of the constraints. More specifically, two constraint removal schemes are introduced, one greedy and the other randomized, and a comparison between them is provided in a detailed computational study in portfolio selection. Other practical aspects of the procedures are also discussed. The removal schemes proposed in this paper are generalizable to a wide range of practical problems.