NDLI: Optimal closing of a pair trade with a model containing jumps

Content Provider	Springer Nature Link
Author	Larsson, Stig Warfheimer, Marcus Lindberg, Carl
Copyright Year	2013
Abstract	A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an Ornstein-Uhlenbeck type process, driven by a Lévy process of finite activity. We prove a necessary condition for optimality (a so-called verification theorem), which takes the form of a free boundary problem for an integro-differential equation. We analyze a finite element method for this problem and prove rigorous error estimates, which are used to draw conclusions from numerical simulations. In particular, we present strong evidence for the existence and uniqueness of an optimal solution.
Ending Page	268
Page Count	20
Starting Page	249
File Format	PDF
ISSN	08627940
e-ISSN	15729109
Journal	Applications of Mathematics
Issue Number	3
Volume Number	58
Language	English
Publisher	Springer-Verlag
Publisher Date	2013-06-16
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	optimal stopping ApplicationMathematics/Computational Methods of Engineering Portfolio theory Theoretical, Mathematical and Computational Physics Ornstein-Uhlenbeck type process Optimization Classical Continuum Physics error estimate pairs trading finite element method Integro-ordinary differential equations Analysis Applications of Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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