A Finite Element like Scheme for Integro-Partial Differential Hamilton-Jacobi-Bellman Equations

Abstract. We construct a finite element like scheme for fully non-linear integro-partial differ-ential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in Finance. The schemes are monotone and robust. We prove that they converge in very general situations, including degenerate equa-tions, multiple dimensions, relatively low regularity of the data, and for most (if not all) types of jump-models used in Finance. In all cases we provide (probably optimal) error bounds. These bounds apply when grids are unstructured and integral terms are very singular, two features that are new or highly unusual in this setting. 1