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

Shuai Jing

Stochastic Processes and their Applications, 2013, vol. 123, issue 2, 300-328

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.

Keywords: Backward stochastic differential equations; Brownian motion; Poisson random measure; Time change; Kulik transformation; Lipschitz continuity; Semiconcavity; Viscosity solution; Value function (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:2:p:300-328

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DOI: 10.1016/j.spa.2012.09.012

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