We extend a linear version of the liquidity risk model of Cetin et al. (2004) to allow for price impacts. We show that the impact of a market order on prices depends on the size of the transaction and the level of liquidity. We obtain a simple characterization of self-financing trading...

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

Consider a d-dimensional Brownian motion X (Xl, ... ,Xd ) and a function F which belongs locally to the Sobolev space W 1,2. We prove an extension of Ito's formula where the usual second order terms are replaced by the quadratic covariations [fk(X), Xkj involving the weak first partial...

In this paper we study an incomplete Brownian motion market and use filtration reduction to obtain a complete market, and hence a unique pricing measure. We then uplift the obtained measure to the original market and study valuation and hedging via the uplifted measure. We show how a general...