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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
Author(s) -
Charalambous K.,
Sophocleous C.,
O'Hara J. G.,
Leach P. G. L.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3383
Subject(s) - mathematics , extension (predicate logic) , context (archaeology) , partial differential equation , homogeneous space , optimal control , nonlinear system , stochastic control , terminal (telecommunication) , control (management) , mathematical optimization , mathematical analysis , computer science , paleontology , physics , geometry , quantum mechanics , artificial intelligence , biology , programming language , telecommunications
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. Copyright © 2014 JohnWiley & Sons, Ltd.