We study the optimal investment problem in a price impact model where multiple market makers compete to satisfy large investor demand. In the case where the market makers have CARA preferences, we show for general large investor utility functions and random endowments that the optimal investment problem with price impact coincides with that in a fictitious market with no price impact, but with random trading constraints. Simple examples show the constraint set need not be either closed or convex. Furthermore, in the one-dimensional case we identify a dichotomy: either the constraint is non-binding, or for certain times and states, the large investor is induced to submit an infinite demand order. We prove additionally that if the large investor and market maker endowments are securitized, then it is optimal for them to make a one time trade at time zero and hence continuous trading is not necessary. Lastly, in the non-binding constraint case, we consider the problem of contingent claim pricing and optimal demand in a segmented economy. We provide explicit formulas for the utility indifference price, and show that optimal derivative demand is inversely proportional to the market maker risk aversion. Thus, in the limit of a large number of market makers (or one risk neutral market maker) optimal demands become large, even taking price impact into account.
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