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Title: Utility maximization under trading constraints with discontinuous utility
Authors: Bian, B
Chen, X
Xu, ZQ 
Issue Date: 2019
Source: SIAM journal on financial mathematics, 2019, v. 10, no. 1, p.243-260
Abstract: This paper investigates a utility maximization problem in a Black–Scholes market, in which trading is subject to a convex cone constraint and the utility function is not necessarily continuous or concave. The problem is initially formulated as a stochastic control problem, and a partial differential equation method is subsequently used to study the associated Hamilton–Jacobi–Bellman equation. The value function is shown to be discontinuous at maturity (with the exception of trivial cases), and its lower-continuous envelope is shown to be concave before maturity. The comparison principle shows that the value function is continuous and coincides with that of its concavified problem.
Keywords: Convex cone constraint
Discontinuous utility function
Stochastic control
Variational inequality
Viscosity solution
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on financial mathematics 
EISSN: 1945-497X
DOI: 10.1137/18M1174659
Rights: © 2019, Society for Industrial and Applied Mathematics
Posted with permission of the publisher.
The following publication Bian, B., Chen, X., & Xu, Z. Q. (2019). Utility Maximization Under Trading Constraints with Discontinuous Utility. SIAM Journal on Financial Mathematics, 10(1), 243-260 is available at
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