On dynamic deviation measures and continuous-time portfolio optimization

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Title: On dynamic deviation measures and continuous-time portfolio optimization
Authors: Pistorius, MR
Stadje, M
Item Type: Journal Article
Abstract: In this paper we propose the notion of dynamic deviation measure , as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition, dynamic deviation measures are characterised as the solutions to a certain class of stochastic differential equations. We establish for any dynamic deviation measure an integral representation, and derive a dual characterisation result in terms of additively m -stable dual sets. Using this notion of dynamic deviation measure we formulate a dynamic mean-deviation portfolio optimization problem in a jump-diffusion setting and identify a subgame-perfect Nash equilibrium strategy that is linear as function of wealth by deriving and solving an associated extended HJB equation.
Date of Acceptance: 18-Feb-2017
URI: http://hdl.handle.net/10044/1/44822
ISSN: 1050-5164
Publisher: Institute of Mathematical Statistics (IMS)
Journal / Book Title: Annals of Applied Probability
Copyright Statement: This paper is embargoed until publication.
Keywords: Statistics & Probability
0102 Applied Mathematics
0104 Statistics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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