On a stochastic differential equation arising in a price impact model

Abstract

We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in a price impact model. These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.Comment: 20 pages. Keywords: Clark-Ocone formula, large investor, Malliavin derivative, Pareto allocation, price impact, Sobolev's embedding, stochastic differential equation; a couple of minor editorial corrections to make it identical to the paper accepted to Stochastic Processes and Their Application