Hamilton-Jacobi-Bellman Equations
نویسنده
چکیده
This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is presented: a novel finite element method is proposed and analysed; several new results on the solubility and solution algorithms of discretised Hamilton-Jacobi-Bellman equations are demonstrated and new results on envelopes are presented.
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