  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.
