Optimal positioning in derivative securities

We consider a simple single period economy in which agents invest so as to maximize expected utility of terminal wealth. We assume the existence of three asset classes, namely a riskless asset #the bond#, a single risky asset #the stock#, and European options of all strikes #derivatives#. In this setting, the inability to trade continuously potentially induces investment in all three asset classes. We consider both a partial equilibrium where all asset prices are initially given, and a more general equilibrium where all asset prices are endogenously determined.