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Optimal liquidation in a limit order book for a risk-averse investor

Lokka, Arne (2014) Optimal liquidation in a limit order book for a risk-averse investor. Mathematical Finance, 24 (4). pp. 696-727. ISSN 0960-1627

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Abstract

In a limit order book model with exponential resilience, general shape function, and an unaffected stock price following the Bachelier model, we consider the problem of optimal liquidation for an investor with constant absolute risk aversion. We show that the problem can be reduced to a two-dimensional deterministic problem which involves no buy orders. We derive an explicit expression for the value function and the optimal liquidation strategy. The analysis is complicated by the fact that the intervention boundary, which determines the optimal liquidation strategy, is discontinuous if there are levels in the limit order book with relatively little market depth. Despite this complication, the equation for the intervention boundary is fairly simple. We show that the optimal liquidation strategy possesses the natural properties one would expect, and provide an explicit example for the case where the limit order book has a constant shape function.

Item Type: Article
Official URL: http://onlinelibrary.wiley.com/journal/10.1111/(IS...
Additional Information: © 2013 Wiley Periodicals, Inc
Library of Congress subject classification: H Social Sciences > HG Finance
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 18 Jun 2013 16:16
URL: http://eprints.lse.ac.uk/50783/

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