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Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions

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Abstract

We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jump-diffusion processes, which are fully nonlinear integro-partial differential equations. Two main results are obtained: (i) error bounds for a class of monotone approximation schemes, which under some assumptions includes finite difference schemes, and (ii) bounds on the error induced when the original Lévy measure is replaced by a finite measure with compact support, an approximation process that is commonly used when designing numerical schemes for integro-partial differential equations. Our proofs use and extend techniques introduced by Krylov and Barles-Jakobsen.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science Technology, 7491, Trondheim, Norway

    Espen R. Jakobsen

  2. Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Kenneth H. Karlsen

  3. Capitalia - Linea Finanza, Prodotti e Canali, Quantitative Finance, Via G. Paisiello 5, 00198, Rome, Italy

    Claudia La Chioma

Authors
  1. Espen R. Jakobsen
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  2. Kenneth H. Karlsen
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  3. Claudia La Chioma
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Correspondence to Kenneth H. Karlsen.

Additional information

This work is supported by the European network HYKE, contract HPRN-CT-2002-00282. The research of E. R. Jakobsen is supported by the Research Council of Norway through grant no 151608/432. The research of K. H. Karlsen is supported by an Outstanding Young Investigators Award from the Research Council of Norway. This work was done while C. La Chioma visited the Centre of Mathematics for Applications (CMA) at the University of Oslo, Norway.

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Jakobsen, E.R., Karlsen, K.H. & La Chioma, C. Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions. Numer. Math. 110, 221–255 (2008). https://doi.org/10.1007/s00211-008-0160-z

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