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# Portfolio Selection Under Conditions of Variable Weights

• Keykhaei, R., Jahandideh M. T. (2012) * Tangency Portfolio in the LP Solvable Portfolio Selection Models.* Published in ** RAIRO - Operation Research** Vol. 46-2, Pages 1505-1515.

In this paper we generalize the single-period Markowitz Mean-Variance portfolio selection problem. The Markowitz's model requires that after choosing the number of each security which constructs the portfolio in the beginning of the investment period, these numbers remain constant during and at the end of the investment period. We drop this assumption and consider an investment model in which the number of each security can vary randomly during the investment period. Indeed we consider a single-period investment with the property that the initial weight of each security is not equal to the final weight of that security. We redefine the notion of the rate of return of each security and show that the return of the investment in a cash account is not certain. We investigate some alternatives among risky securities which acts similar to cash accounts. For this we introduce the notion of { free} security and relate free securities to a riskless security.