Dynamic convex duality in constrained utility maximization

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Title: Dynamic convex duality in constrained utility maximization
Authors: Li, Y
Zheng, H
Item Type: Journal Article
Abstract: In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of forward and backward stochastic differential equations (FBSDEs) plus some additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. We also find that the optimal wealth process coincides with the adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems, which contrasts the simplicity of the duality approach we propose and the technical complexity of solving the primal problem directly.
Issue Date: 25-Jun-2018
Date of Acceptance: 20-May-2018
URI: http://hdl.handle.net/10044/1/60922
DOI: https://doi.org/10.1080/17442508.2018.1480023
ISSN: 1744-2508
Publisher: Taylor & Francis
Start Page: 1145
End Page: 1169
Journal / Book Title: Stochastics: An International Journal of Probability and Stochastic Processes
Volume: 90
Issue: 8
Copyright Statement: © 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastics: An International Journal of Probability and Stochastic Processes on 25 Jun 2018 available online: https://www.tandfonline.com/doi/full/10.1080/17442508.2018.1480023
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Statistics & Probability
Mathematics
Convex duality
primal and dual FBSDEs
utility maximization
convex portfolio constraints
STOCHASTIC MAXIMUM PRINCIPLE
OPTIMIZATION PROBLEMS
INCOMPLETE MARKETS
PORTFOLIO POLICIES
CONSUMPTION
MODEL
INVESTMENT
SELECTION
SYSTEMS
Statistics & Probability
01 Mathematical Sciences
15 Commerce, Management, Tourism and Services
Publication Status: Published
Online Publication Date: 2018-06-25
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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