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PreprintarXiv licencearXiv

Duality for Stochastic Control with non-Markovian Random Coefficients

  • Peter Bank
  • Jannis R. Dause
  • Filippo de Feo
  • Peter K. Friz
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Abstract

We develop novel duality methods for stochastic optimal control problems under two sources of randomness and non-Markovian random coefficients adapted to just one of them. The Hamilton-Jacobi-Bellman (HJB) equation is a second-order backward stochastic partial differential equation. Our duality theory provides an alternative description of the random value function in terms of a suitable pathwise optimal control problem parameterized by the realizations of one of the Brownian motions. This allows us to regain Markovianity using the theory of rough optimal control problems, leading to rough second order HJB equations that we solve in a suitable viscosity sense.

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Cite

BibTeXRIS
BibTeX
@misc{bank2026duality,
  title = {{Duality for Stochastic Control with non-Markovian Random Coefficients}},
  author = {Peter Bank and Jannis R. Dause and Filippo de Feo and Peter K. Friz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05101},
  eprint = {2609.05101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05101},
}
RIS
TY  - UNPB
TI  - Duality for Stochastic Control with non-Markovian Random Coefficients
AU  - Peter Bank
AU  - Jannis R. Dause
AU  - Filippo de Feo
AU  - Peter K. Friz
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05101
UR  - https://arxiv.org/abs/2609.05101
AB  - We develop novel duality methods for stochastic optimal control problems under two sources of randomness and non-Markovian random coefficients adapted to just one of them. The Hamilton-Jacobi-Bellman (HJB) equation is a second-order backward stochastic partial differential equation. Our duality theory provides an alternative description of the random value function in terms of a suitable pathwise optimal control problem parameterized by the realizations of one of the Brownian motions. This allows us to regain Markovianity using the theory of rough optimal control problems, leading to rough second order HJB equations that we solve in a suitable viscosity sense.
ER  -