# Constrained portfolio liquidation in a limit order book model

Aurélien Alfonsi; Antje Fruth; Alexander Schied

Banach Center Publications (2008)

- Volume: 83, Issue: 1, page 9-25
- ISSN: 0137-6934

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topAurélien 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 -

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