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<p>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.</p>

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S-shaped Utility Maximization with VaR Constraint and Partial Information

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月25日

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  • Dongmei Zhu,
  • Ashley Davey,
  • Harry Zheng

摘要

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.