Abstract:

Under multi-probability distribution cluster, equivalence of multi-loss WCVaR (Worst Conditional Value-at-Risk, MCVaR) problem is studied. According to the VaR measure under multi-probability distribution cluster, the multi-objective optimization problem (MWCVaR) is defined by the WCVaR risk measurement. It is proved that the optimization problem (MWCVaR) is equivalent to solve another multi-objective optimization problem. In the case of a finite distributions cluster, under certain conditions, we prove that the Pareto effective solution of the problem (MWCVaR) can be approximated by a finite distributions cluster.

Key words: multi-objective conditional value at risk, MWCVaR, probability distribution cluster, equivalent optimization theorem