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<p>In utility maximization with non-Markovian setting, the value function satisfies a stochastic Hamilton-Jacobi-Bellman (HJB) equation, a fully nonlinear backward stochastic partial differential equation (BSPDE). We propose iterative deep learning algorithms for such BSPDEs and analyze their convergence. We derive the error estimate of the time discretization scheme for BSPDEs, that of the policy iteration scheme for discretized BSPDEs, and that of the iterative deep learning scheme for discretized BSPDEs. We also test the algorithms and show their convergence and accuracy with numerical examples, including Markovian Heston volatility model and non-Markovian rough volatility model.</p>

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Convergence Analysis of Iterative Deep Learning Algorithms for Fully Nonlinear BSPDEs in Non-Markovian Utility Maximization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Jingtang Ma,
  • Haofei Wu,
  • H. Harry Zheng

摘要

In utility maximization with non-Markovian setting, the value function satisfies a stochastic Hamilton-Jacobi-Bellman (HJB) equation, a fully nonlinear backward stochastic partial differential equation (BSPDE). We propose iterative deep learning algorithms for such BSPDEs and analyze their convergence. We derive the error estimate of the time discretization scheme for BSPDEs, that of the policy iteration scheme for discretized BSPDEs, and that of the iterative deep learning scheme for discretized BSPDEs. We also test the algorithms and show their convergence and accuracy with numerical examples, including Markovian Heston volatility model and non-Markovian rough volatility model.