This paper studies the effects of price impact upon optimal investment , as well as the pricing of, and demand for, derivative contracts. Assuming market makers have exponential preferences, we show for general utility functions that a large investor's optimal investment problem with price impactcan be re-expressed as a constrained optimization problem in fictitious market without price impact. While typically the (random) constraint set is  neither closed nor convex , in several important cases of interest, the constraint is non-binding. In these instances, we explicitly identify optimal demands for derivative contracts, and state three notions of an arbitrage free price . Due to price impact, even if a price is not arbitrage free, the resulting arbitrage opportunity only exists for limited position sizes, and might be ignored because of hedging considerations. Lastly, in a segmented market where large investors interact with local market makers, we show equilibrium positions in derivative contracts are inversely proportional to the market makers' representative risk aversion. Thus , large positions endogenously arise either as market makers approach risk neutrality, or as the number of market makers becomes large .
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies , as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex . Regarding hedging, non-linear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore , large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers .
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effects of price impact upon optimal investment
optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies
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the pricing of, and demand for, derivative contracts. Assuming market makers have exponential
both pricing rules and demand schedules for contingent claims. For exponential market makers
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show for general utility functions that a large investor's optimal investment problem with price impactcan be re-expressed as a constrained optimization problem in fictitious market without price impact. While typically
establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where
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generically
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, in several important cases of interest, the constraint is non-binding. In these instances, we explicitly identify optimal demands for derivative contracts, and state three notions of an arbitrage free price . Due to price impact, even if a price is not arbitrage free, the resulting arbitrage opportunity only exists
. Regarding hedging, non-linear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only
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Lastly, in a segmented market where large investors interact with local market makers, we show equilibrium positions in derivative contracts
We also show that arbitrage inducing prices may arise endogenously in equilibrium, and that equilibrium positions
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either as market makers approach
in the limit of either market maker
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