Regularity of the value function for a two-dimensional singular stochastic control problem

H. Mete Soner, Steven E. Shreve

Research output: Contribution to journalArticle

60 Scopus citations

Abstract

It is desired to control a two-dimensional Brownian motion by adding a (possibly singularly) continuous process to it so as to minimize an expected infinite-horizon discounted running cost. The Hamilton-Jacobi-Bellman characterization of the value function V is a variational inequality which has a unique twice continuously differentiable solution. The optimal control process is constructed by solving the Skorokhod problem of reflecting the two-dimensional Brownian motion along a free boundary in the -▽ V direction.

Original languageEnglish (US)
Pages (from-to)876-907
Number of pages32
JournalSIAM Journal on Control and Optimization
Volume27
Issue number4
DOIs
StatePublished - 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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