We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a time-dependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results solve the problem of minimizing the expected liquidity costs within a given convex set of predictable trading strategies by reducing it to a deterministic optimization problem. This deterministic problem is explicitly solved for the case in which the convex set of strategies is defined via finitely many linear constraints. A detailed study of optimal portfolio liquidation in markets with opening and closing call auctions is provided as an illustration. We also obtain closed-form solutions for the unconstrained portfolio liquidation problem in our time-inhomogeneous setting and thus extend a result from our earlier paper [1].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-1,
author = {Aur\'elien Alfonsi and Antje Fruth and Alexander Schied},
title = {Constrained portfolio liquidation in a limit order book model},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {9-25},
zbl = {1154.91407},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-1}
}
Aurélien Alfonsi; Antje Fruth; Alexander Schied. Constrained portfolio liquidation in a limit order book model. Banach Center Publications, Tome 83 (2008) pp. 9-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-1/