文档介绍：UTLogo100Stochastic ProgrammingSchool of Management, UCASPortfolio Selection ModelKai YaoSchool of Management, UCASKai ******@ ProgrammingSchool of Management, UCASPortfolio SelectionAssume there arendi?erent securities in the market, whose uncertain return-s are random variablesξ1, ξ2,· · ·, ξn. A portfolio is an investment fraction(β1, β2,· · ·, βn) such thatβ1+β2+· · ·+βn= 1. The investment return isξ=β1ξ1+β2ξ2+· · ·+ selection problem concerns ?nding the optimal portfolio (β1, β2,· · ·, βn) under some ******@ ProgrammingSchool of Management, UCASMean-Variance Model (Harry Markowitz)???????????????maxβiE[β1ξ1+β2ξ2+· · ·+βnξn]subject to:V[β1ξ1+β2ξ2+· · ·+βnξn]≤V0β1+β2+· · ·+βn= 1βi≥ ******@ ProgrammingSchool of Management, UCASVariant: Model-I???????????????maxβiE[U(β1ξ1+β2ξ2+· · ·+βnξn)]subject to:V[β1ξ1+β2ξ2+· · ·+βnξn]≤V0β1+β2+· · ·+βn= 1βi≥0,whereUis a utility ******@ ProgrammingSchool of Management, UCASVariant: Model-II?????????????????????maxβiE0subject to:Pr{β1ξ1+β2ξ2+· · ·+βnξn≥E0} ≥αV[β1ξ1+β2ξ2+· · ·+βnξn]≤V0β1+β2+· · ·+βn= 1βi≥ ******@ ProgrammingSchool of Management, UCASVariant: Model-III???????????????minβiV[β1ξ1+β2ξ2+· · ·+βnξn]subject to:E[β1ξ1+β2ξ2+· · ·+βnξn]≥E0β1+β2+· · ·+βn= 1βi≥ ******@ ProgrammingSchool of Management, UCASRisk MeasureThe risk measure of a portfolio is de?ned byR(β1, β2,· · ·, βn) = max1≤i≤nβiE[|ξi?E[ξi]|].???????????????maxβiE[β1ξ1+β2ξ2+· · ·+βnξn]subject to:R(β1, β2,· · ·, βn)≤R0β1+β2+· · ·+βn= 1βi≥ ******@ ProgrammingSchool of Management, UCASSemi-VarianceThe semi-variance ofξis de?ned asSV[ξ] =E[((ξ?E[ξ])?)2].???????????????maxβiE[β1ξ1+β2ξ2+· · ·+βnξn]subject to:SV[β1ξ1+β2ξ2+· · ·+βnξn]≤SV0β1+β2+· · ·+βn= 1βi≥ ******@ ProgrammingSchool of Mana