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

  • Harold A. Moreno-FrancoEmail author


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.


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

Mathematics Subject Classification

49L99 45K05 93E20 



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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