Marginalriskrepresentstheriskcontributionofaninpidualassettotheriskoftheentireportfolio.Inthispaper,weinvestigatetheportfolioselectionproblemwithdirectmarginalriskcontrolinalinearconicprogrammingframework.'Theoptimizationmodelinvolvedisanonconvexquadraticallyconstrainedquadraticprogramming(QCQP)problem.WefirsttransformtheQCQPproblemintoalinearconicprogrammingproblem,andthenapproximatetheproblembysemidefiniteprogramming(SDP)relaxationproblemsoversomesubrectangles.InordertoimprovethelowerboundsobtainedfromtheSDPrelaxationproblems,linearandquadraticpolarcutsareintroducedfordesigningabranch-and-cutalgorithm,thatmayyieldane-optimalglobalsolution(withrespecttofeasibilityandoptimality)inafinitenumberofiterations.ByexploringthespecialstructureoftheSDPrelaxationproblems,anadaptivebranch-and-cutruleisemployedtospeedupthecomputation.Theproposedalgorithmistestedandcomparedwithaknownmethodintheliteratureforportfolioselectionproblemswithhundredsofassetsandtensofmarginalriskcontrolconstraints.
