Abstracts

Liquidity in financial markets usually is not constant – it varies randomly in time and sometimes faces shocks. We consider the problem of closing a large asset position in a market with stochastic temporary price impact. We provide a probabilistic solution of the associated control problem by means of a Backward Stochastic Differential Equation (BSDE). The novelty of the solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists and perform a verification. For special cases we determine optimal trading strategies explicitly.