The Convergence of Set-Valued Scenario Approach for Downside Risk Minimization

Scenario approach is a widely used tool in portfolio risk management,however,it often runs into dilemma when determining the distribution of asset returns with insufficient information,which will be used to simulate the scenarios.Also the quality of generated scenarios are not guaranteed even when the distribution of asset returns is known exactly.A set-valued scenario approach was proposed by Zhu,et al.(2015)as a possible remedy.As a necessary supplement of the results proposed by Zhu,et al.(2015),this paper theoretically investigates the convergent property of the numerical solution based on the set-valued scenario approach under the condition that the underlying distribution is known.