Portfolio Management and the Shrinking Knapsack Algorithm

Since the formulation of the portfolio selection problem by Markowitz [12] as a parametric quadratic programming problem, considerable effort has been devoted to obtaining operational portfolio management models. Research has involved: (1) characterizing the return generating process in terms of index models; (2) specifying special-purpose algorithms such as the critical-line method of Markowitz [13] or the solution procedure of Jucker and de Faro [11]; (3) using linear programming formulations to approximate solutions to the nonlinear programming problems such as Sharpe [20, 22] and Stone [25]; and (4) converting portfolio selection models into portfolio management models designed to revise an existing protfolio subject to transaction costs using heuristics such as Smith [24] or revision formulations such as Pogue [16, 17] and Stone and Reback [27].