A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems
نویسندگان
چکیده
Abstract Stochastic optimal principle leads to the resolution of a partial differential equation (PDE), namely Hamilton–Jacobi–Bellman (HJB) equation. In general, this cannot be solved analytically, thus numerical algorithms are only tools provide accurate approximations. The aims paper is introduce novel fitted finite volume method solve high dimensional degenerated HJB from stochastic control problems in dimension ( $$ n\ge 3$$ n ≥ 3 ). challenge here due nature our which second-order coupled with an optimization problem. For such problems, standard scheme as difference losses its monotonicity and therefore convergence toward viscosity solution may not guarantee. We discretize using method, well known tackle PDEs, while time discretisation performed Implicit Euler scheme.. show that matrices resulting spatial discretization temporal M-matrices. Numerical results finance demonstrating accuracy proposed comparing provided.
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ژورنال
عنوان ژورنال: Computational Economics
سال: 2021
ISSN: ['1572-9974', '0927-7099']
DOI: https://doi.org/10.1007/s10614-021-10197-4