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A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time-dependent parameters

Charalambous, K and Sophocleous, C and O'Hara, JG and Leach, PGL (2015) 'A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time-dependent parameters.' Mathematical Methods in the Applied Sciences, 38 (17). 4448 - 4460. ISSN 0170-4214

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Abstract

Copyright © 2014 John Wiley & Sons, Ltd. In a fairly recent paper (2008 American Control Conference, June 11-13, 1035-1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal-value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution.

Item Type: Article
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 15 May 2015 15:37
Last Modified: 22 Jan 2019 03:15
URI: http://repository.essex.ac.uk/id/eprint/13704

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