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@article{li:2018:10.1080/17442508.2018.1480023,
author = {li, Y and Zheng, H},
doi = {10.1080/17442508.2018.1480023},
journal = {Stochastics: An International Journal of Probability and Stochastic Processes},
pages = {1145--1169},
title = {Dynamic convex duality in constrained utility maximization},
url = {http://dx.doi.org/10.1080/17442508.2018.1480023},
volume = {90},
year = {2018}
}

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TY  - JOUR
AB  - 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.
AU  - li,Y
AU  - Zheng,H
DO  - 10.1080/17442508.2018.1480023
EP  - 1169
PY  - 2018///
SN  - 1744-2508
SP  - 1145
TI  - Dynamic convex duality in constrained utility maximization
T2  - Stochastics: An International Journal of Probability and Stochastic Processes
UR  - http://dx.doi.org/10.1080/17442508.2018.1480023
UR  - https://www.tandfonline.com/doi/full/10.1080/17442508.2018.1480023
UR  - http://hdl.handle.net/10044/1/60922
VL  - 90
ER  -

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