Evolving constrained mean-VaR efficient frontiers

Value-at-Risk - an industry standard risk measure; may be applied to assess and optimize a portfolio of assets. However, traditional optimization software does not provide for value-at-risk optimization. One solution is to apply evolutionary techniques to search for optimal solutions. However, to increase the realism in evolutionary solutions, it is important to consider the inclusion of realistic real-world constraints and to further consider the effect of the initialization scheme on the results achievable. Two techniques are investigated in this work. The key technique is multi-objective differential evolution (MODE) which is applied together with an adapted initialization scheme to search for VaR-optimal portfolios in the presence of real-world constraints. Further, NSGA-II - a more established multi-objective optimization technique; is implemented and extended with real world constraints and a refined initialization scheme, so as to compare the benefits of the MODE technique in the light of a refined NSGA-II technique and highlight the benefits of such refinements on NSGA-II itself.