S-shaped Utility Maximization with VaR Constraint and Partial Information

Dongmei Zhu, Ashley Davey and Harry Zheng

Papers from arXiv.org

Abstract: We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the problem and compare their performances with numerical examples.

Date: 2025-06
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