Date
Thu, 14 Jun 2012
Time
14:00 - 15:00
Location
Gibson Grd floor SR
Speaker
Dr Christoph Reisinger
Organisation
University of Oxford

While a general framework of approximating the solution to Hamilton-Jacobi-Bellman (HJB) equations by difference methods is well established, and efficient numerical algorithms are available for one-dimensional problems, much less is known in the multi-dimensional case. One difficulty is the monotone approximation of cross-derivatives, which guarantees convergence to the viscosity solution. We propose a scheme combining piecewise freezing of the policies in time with a suitable spatial discretisation to establish convergence for a wide class of equations, and give numerical illustrations for a diffusion equation with uncertain parameters. These equations arise, for instance, in the valuation of financial derivatives under model uncertainty.

This is joint work with Peter Forsyth.

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