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S-shaped Utility Maximization with VaR Constraint and Partial Information

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  • Dongmei Zhu
  • Ashley Davey
  • Harry Zheng

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.

Suggested Citation

  • Dongmei Zhu & Ashley Davey & Harry Zheng, 2025. "S-shaped Utility Maximization with VaR Constraint and Partial Information," Papers 2506.10103, arXiv.org.
    • Handle: RePEc:arx:papers:2506.10103
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    File URL: http://arxiv.org/pdf/2506.10103
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