Constrained portfolio liquidation in a limit order book model

Aurélien Alfonsi, Antje Fruth, and Alexander Schied. "Constrained portfolio liquidation in a limit order book model." Banach Center Publications 83.1 (2008): 9-25. <http://eudml.org/doc/281984>.

@article{AurélienAlfonsi2008,
abstract = {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].},
author = {Aurélien Alfonsi, Antje Fruth, Alexander Schied},
journal = {Banach Center Publications},
keywords = {liquidity risk; optimal portfolio liquidation; limit order book with resilience; call auction; market impact model; constrained trading strategies; market order},
language = {eng},
number = {1},
pages = {9-25},
title = {Constrained portfolio liquidation in a limit order book model},
url = {http://eudml.org/doc/281984},
volume = {83},
year = {2008},
}

TY - JOUR
AU - Aurélien Alfonsi
AU - Antje Fruth
AU - Alexander Schied
TI - Constrained portfolio liquidation in a limit order book model
JO - Banach Center Publications
PY - 2008
VL - 83
IS - 1
SP - 9
EP - 25
AB - 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].
LA - eng
KW - liquidity risk; optimal portfolio liquidation; limit order book with resilience; call auction; market impact model; constrained trading strategies; market order
UR - http://eudml.org/doc/281984
ER -