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Efficient price dynamics in a limit order market: an utility indifference approach

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  • Masaaki Fukasawa

Abstract

We construct an utility-based dynamic asset pricing model for a limit order market. The price is nonlinear in volume and subject to market impact. We solve an optimal hedging problem under the market impact and derive the dynamics of the efficient price, that is, the asset price when a representative liquidity demander follows an optimal strategy. We show that a Pareto efficient allocation is achieved under a completeness condi- tion. We give an explicit representation of the efficient price for several examples. In particular, we observe that the volatility of the asset depends on the convexity of an initial endowment. Further, we observe that an asset price crash is invoked by an endowment shock. We establish a dynamic programming principle under an incomplete framework.

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  • Masaaki Fukasawa, 2014. "Efficient price dynamics in a limit order market: an utility indifference approach," Papers 1410.8224, arXiv.org.
    • Handle: RePEc:arx:papers:1410.8224
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    Cited by:

    1. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.

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