How Best to Flip-Flop if You Must: Integer Dynamic Stochastic Programming for Either-Or

Standard portfolio analysis presumes one can blend different securities continuously. When one must choose all of one portfolio or all of another, we are in stochastic digital programming: either-or, zero-or-one choice. The algorithm for doing this optimally is shown to be simpler than in real variable maximizing, a switch from the usual extra complexities of digital programming. The Bellman multi-period dynamic programming is shown, paradoxically, to make it possible for a risk-averse investor to want sometimes to embrace an unfair gamble. The superiority of within-time diversification over across-time diversification carries over to this flip-flop case.