Eur. Phys. J. B 55, 453-459 (2007)
https://doi.org/10.1140/epjb/e2007-00067-9

Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices

Dipartimento di Fisica e Tecnologie Relative, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

Corresponding author: ^a lillo@lagash.dft.unipa.it

Received: 30 November 2006
Revised: 12 February 2007
Published online: 9 March 2007

Abstract

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons.