Viscosity Solution of Optimal Stopping Problem for Stochastic Systems with Bounded Memory

Mou-Hsiung Chang, Tao Pang, Moustapha Pemy
2012 Stochastic Analysis and Applications  
We consider a finite time horizon optimal stopping problem for a system of stochastic functional differential equations with a bounded memory. Under some sufficiently smooth conditions, a Hamilton-Jacobi-Bellman (HJB) variational inequality for the value function is derived via dynamical programming principle. It is shown that the value function is the unique viscosity solution of the HJB variational inequality.
doi:10.1080/07362994.2012.727143 fatcat:7fxm73b45nbqdoxl5kmu3o2hxy