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Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton–Jacobi–Bellman type

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  • Jing, Shuai

Abstract

We study the regularity properties of integro-partial differential equations of Hamilton–Jacobi–Bellman type with the terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a Brownian motion and a compensated Poisson random measure. More precisely, we prove that, under appropriate assumptions, the viscosity solution of such equations is jointly Lipschitz and jointly semiconcave in (t,x)∈Δ×Rd, for all compact time intervals Δ excluding the terminal time. Our approach is based on the time change for the Brownian motion and on Kulik’s transformation for the Poisson random measure.

Suggested Citation

  • Jing, Shuai, 2013. "Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton–Jacobi–Bellman type," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 300-328.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:300-328
    DOI: 10.1016/j.spa.2012.09.012
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    References listed on IDEAS

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    1. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
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