| One of the most prior matter of fnance is to study apply to assets efcientlyand reasonably.In1952,suppose that the gain of stock is a random variable quan-tity，using the proft variance of stock to measure the risk of investment, applyingthe proft mean value of stock to measure the result of income，people advancedvariable quantity and mean value model responding to portfolio.According to theactual situation of securities market,people also found some friction factor：tradingfee and revenue etc, which has direct infuence on investors’ decision,leading toplenty of scholars’ concern on investment portfolio with some friction factor.This essay studied no risk assets loans under the investment portfolio andminimax models of no allowing short selling in fnancial optimize and trading feeunder no allowing short selling, at the same time,the essay analysed both types ofmodels by the mathematical,later on,not only analytical expressions,but the fron-tiers of expression and geometry expressions features were educed efciently.whensolving the later models the essay studied, because trading fee can not be diferen-tial,which brings inconvenient while we solve expressions. As a result, we broughtabout the sub-diferential. According to the defnition of sub-diferential,we gotthe sub-diferential of trading fee function.This essay contains fve chapter, frstly, the frst chapter introduces the studybackground and efects of investment portfolio and the main work of all and in-troduces the basic concept of optimization and denotation used in the text.then,the next three chapters, which analysed the mathematics features of no risk assetsloans under the investment portfolio and minimax problems of no allowing shortselling in fnancial optimize and two kinds of trading fee under no allowing shortselling, consequently,efcient investment portfolio analytical expressions and ex-pressions features were educed,fnally, the ffth chapter is a conclusion, whichconcludes the results and expressed the anticipation of the future. |
