Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/56749
Authors: 
Naujokat, Felix
Horst, Ulrich
Year of Publication: 
2011
Series/Report no.: 
SFB 649 discussion paper 2011-053
Abstract: 
In this article the problem of curve following in an illiquid market is addressed. Using techniques of singular stochastic control, we extend the results of [NW11] to a twosided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. The new feature is that we now get a nondegenerate no-trade region, which implies that market orders are only used when the spread is small. This allows to describe precisely when it is optimal to cross the bid ask spread, which is a fundamental problem of algorithmic trading. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders.
Subjects: 
stochastic maximum principle
convex analysis
fully coupled forward backward stochastic differential equations
trading in illiquid markets
JEL: 
C61
G11
Document Type: 
Working Paper

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