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A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems

Author

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  • Christelle Dleuna Nyoumbi

    (Institut de Mathématiques et de Sciences Physiques de l’Université d’Abomey Calavi)

  • Antoine Tambue

    (Western Norway University of Applied Sciences)

Abstract

Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely the Hamilton–Jacobi–Bellman (HJB) equation. In general, this equation cannot be solved analytically, thus numerical algorithms are the only tools to provide accurate approximations. The aims of this paper is to introduce a novel fitted finite volume method to solve high dimensional degenerated HJB equation from stochastic optimal control problems in high dimension ( $$ n\ge 3$$ n ≥ 3 ). The challenge here is due to the nature of our HJB equation which is a degenerated second-order partial differential equation coupled with an optimization problem. For such problems, standard scheme such as finite difference method losses its monotonicity and therefore the convergence toward the viscosity solution may not be guarantee. We discretize the HJB equation using the fitted finite volume method, well known to tackle degenerated PDEs, while the time discretisation is performed using the Implicit Euler scheme.. We show that matrices resulting from spatial discretization and temporal discretization are M-matrices. Numerical results in finance demonstrating the accuracy of the proposed numerical method comparing to the standard finite difference method are provided.

Suggested Citation

  • Christelle Dleuna Nyoumbi & Antoine Tambue, 2023. "A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 1-34, January.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:1:d:10.1007_s10614-021-10197-4
    DOI: 10.1007/s10614-021-10197-4
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    References listed on IDEAS

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