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Integro-PDE in Hilbert Spaces: Existence of Viscosity Solutions

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Abstract

Existence of a viscosity solution to a non-local Hamilton-Jacobi-Bellman equation in a Hilbert space is established. We prove that the value function of an associated stochastic control problem is a viscosity solution. We provide a complete proof of the Dynamic Programming Principle for the stochastic control problem. We also illustrate the theory with Bellman equations associated to a controlled wave equation and controlled Musiela equation of mathematical finance both perturbed by Lévy processes.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Andrzej Święch

  2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950, Warsaw, Poland

    Jerzy Zabczyk

Authors
  1. Andrzej Święch
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  2. Jerzy Zabczyk
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Correspondence to Andrzej Święch.

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Święch, A., Zabczyk, J. Integro-PDE in Hilbert Spaces: Existence of Viscosity Solutions. Potential Anal 45, 703–736 (2016). https://doi.org/10.1007/s11118-016-9563-0

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  • DOI: https://doi.org/10.1007/s11118-016-9563-0

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