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 nonlinear 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, nonlinear 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.

中文翻译：

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价格影响下的最优投资，衍生品需求和套利

本文研究具有竞争性做市商的基于库存的价格影响模型中的随机end赋的最优投资问题。我们的目标是分析价格影响如何影响最优政策，以及或有索赔的定价规则和需求计划。对于指数做市商的偏好，由于价格的影响，我们建立了两个影响：交易受限和非线性对冲成本。对于前者来说，影响模型中的财富过程与没有影响但具有约束交易的模型中的财富过程相同，其中（随机）约束集通常既不封闭也不凸。关于套期保值，非线性套期保值成本推动了对索赔的无套利价格的研究。我们提供了三个这样的概念，这在无摩擦情况下是一致的，但在价格影响方面却大不相同。此外，我们展示了套利机会，如果它们是由索赔价格引起的，则只能用于有限的头寸规模，如果被避险因素压倒，可能会被忽略。我们还表明，套利诱导的价格可能在均衡中内生，均衡位置与做市商的代表性风险厌恶成反比。因此，在做市商风险中性或大量做市商的极限内生产生大量头寸。我们还表明，套利诱导的价格可能在均衡中内生，均衡位置与做市商的代表性风险厌恶成反比。因此，在做市商风险中性或大量做市商的极限内生产生大量头寸。我们还表明，套利诱导的价格可能在均衡中内生，均衡位置与做市商的代表性风险厌恶成反比。因此，在做市商风险中性或大量做市商的极限内生产生大量头寸。