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Viscosity Solutions to HJB Equations with Hölder Continuous Coefficients

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Listed:
  • Jianrui Li

    (Tianjin University)

  • Jinghai Shao

    (Tianjin University)

  • Hui Zhao

    (Nankai University)

Abstract

This work studies the optimal control problem for diffusion processes with Hölder continuous coefficients. Based on Meyer–Tanaka’s formula, we establish an estimate on the local times of controlled diffusion processes, which enables us to provide a new estimate on the regularity of the value function. Then, the value function can be characterized as a unique viscosity solution of certain HJB equation.

Suggested Citation

  • Jianrui Li & Jinghai Shao & Hui Zhao, 2025. "Viscosity Solutions to HJB Equations with Hölder Continuous Coefficients," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-15, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02665-w
    DOI: 10.1007/s10957-025-02665-w
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    References listed on IDEAS

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    7. Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
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