English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the stochastic optimal control problem for jumpdiffusion systems with state constraints. In general, the value function ofsuch problems is a discontinuous viscosity solution of theHamilton-Jacobi-Bellman (HJB) equation, since the regularity cannot beguaranteed at the boundary of the state constraint. By adapting approaches of\cite{Bokanowski_SICON_2016} and the stochastic target theory, we obtain anequivalent representation of the original value function as the backwardreachable set. We then show that this backward reachable can be characterizedby the zero-level set of the auxiliary value function for the unconstrainedstochastic control problem, which includes two additional unbounded controls asa consequence of the martingale representation theorem. We prove that theauxiliary value function is a unique continuous viscosity solution of theassociated HJB equation, which is the second-order nonlinear integro-partialdifferential equation (IPDE). Our paper provides an explicit way tocharacterize the original (possibly discontinuous) value function as azero-level set of the continuous solution of the auxiliary HJB equation. Theproof of the existence and uniqueness requires a new technique due to theunbounded control sets, and the presence of the singularity of thecorresponding L\'evy measure in the nonlocal operator of the HJB equation.

Backward Reachability Approach to State-Constrained Stochastic Optimal Control Problems for Jump Diffusion Systems