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Applied Mathematics & Optimization

, Volume 78, Issue 1, pp 25–60 | Cite as

Solution to HJB Equations with an Elliptic Integro-Differential Operator and Gradient Constraint

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Abstract

The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton–Jacobi–Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a controlled d-dimensional Lévy process.

Keywords

HJB equation NIDD problem Integro-differential operator Stochastic control problem Lévy process 

Mathematics Subject Classification

49L99 45K05 93E20 

Notes

Acknowledgements

The results in this paper are part of the Ph.D. thesis of the author H. A. Moreno-Franco [31], under the supervision of Dr. Daniel Hernández-Hernández and Dr. Víctor Rivero. The author would like to thank: CONACyT and CIMAT for the Ph.D. fellowship and facilities provided; National Research University Higher School of Economics for the financial support in finishing this project; his doctoral advisors of thesis Dr. Daniel Hernández-Hernández and Dr. Víctor Rivero, for their guidance on this work; and finally, his readers of thesis Dr. Jose Luis Menaldi, Dr. Renato Iturriaga, Dr. Hector Sanchez and Dr. Juan Carlos Pardo, for their advice and suggestions.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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