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

K. Charalambous, C. Sophocleous, J. G. O'Hara, P. G.L. Leach

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)4448-4460
Number of pages13
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number17
DOIs
Publication statusPublished - 30 Nov 2015

Keywords

  • evolution partial differential equations
  • financial mathematics
  • Lie symmetries
  • stochastic control

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