Processing second-order stochastic dominance models using cutting-plane representations

Novel approaches for portfolio construction using second order stochastic dominance

“…, S Sτ S ). Using a cutting plane representation (Fábián et al 2011a) the model can be written as: max V…”

“…Remark 2 The cutting plane formulation above has a huge number of constraints (3), referred to in Fábián et al (2011a) as "cuts". The specialised solution method (Fábián et al 2011a) adds cuts at each iteration until optimality is reached; it is shown that in practice, only a few cuts are needed.…”

“…The specialised solution method (Fábián et al 2011a) adds cuts at each iteration until optimality is reached; it is shown that in practice, only a few cuts are needed. For example, all models with 10,000 scenarios of assets returns were solved with less than 30 iterations.…”

“…For example, all models with 10,000 scenarios of assets returns were solved with less than 30 iterations. For more details, the reader is referred to Fábián et al (2011a).…”

“…This term was dropped in the cutting plane formulation, the advantage of this being huge decrease in computational difficulty and solution time; just as an example, models with tens of thousands of scenarios were solved within seconds, while the original model formulation in Roman et al (2006) could only deal with a number of scenarios in the order of hundreds. In Fábián et al (2011a), extensive computational results are reported. For relatively small datasets, SSD models were solved with both the cutting plane formulation and the original formulation including the regularisation term; in all instances, both formulations led to the same optimal solutions.…”