# Abstracts

**A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions**

*Jinniao Qiu (Humboldt Universität zu Berlin, Germany)*

Thursday June 5, 14:00-14:30 | session 8.8 | Trading (Strategies) | room 1+2

We establish existence and regularity results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of a non-Markovian stochastic control optimal problem in which the terminal state of the controlled process is prespecified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.

**Optimal position closure in a market with stochastic price impact**

*Thomas Kruse (Université d'Evry, France)*

Thursday June 5, 14:30-15:00 | session 8.8 | Trading (Strategies) | room 1+2

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.

**Smooth solutions to portfolio liquidation problems under price-sensitive market impact**

*Paulwin Graewe (Humboldt-Universität zu Berlin, Germany)*

Thursday June 5, 15:00-15:30 | session 8.8 | Trading (Strategies) | room 1+2

We establish existence and uniqueness of a classical solution to a semilinear parabolic partial differential equation with singular initial condition. This equation describes the value function of the control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs associated with dark pool trading. We establish the explicit asymptotic behavior of the value function at the terminal time and give the optimal trading strategy in feedback form.