Constrained quadratic risk minimization via forward and backward stochastic differential equations

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Title: Constrained quadratic risk minimization via forward and backward stochastic differential equations
Authors: Li, Y
Zheng, H
Item Type: Journal Article
Abstract: In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of forward and backward stochastic differential equations (FBSDEs) together with other conditions. We characterize explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion, and vice versa. We apply the results to solve quadratic risk minimization problems with cone constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems.
Issue Date: 1-Apr-2018
Date of Acceptance: 17-Jan-2018
URI: http://hdl.handle.net/10044/1/57918
DOI: https://dx.doi.org/10.1137/15M1052457
ISSN: 0363-0129
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1130
End Page: 1153
Journal / Book Title: SIAM Journal on Control and Optimization
Volume: 56
Issue: 2
Copyright Statement: © 2018, Society for Industrial and Applied Mathematics
Keywords: Science & Technology
Technology
Physical Sciences
Automation & Control Systems
Mathematics, Applied
Mathematics
convex duality
primal and dual FBSDEs
stochastic linear quadratic control
random coefficients
control constraints
RANDOM-COEFFICIENTS
UTILITY MAXIMIZATION
PORTFOLIO SELECTION
INCOMPLETE MARKETS
OPTIMAL INVESTMENT
CONVEX DUALITY
0102 Applied Mathematics
0906 Electrical And Electronic Engineering
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status: Published
Online Publication Date: 2018-03-27
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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