# Help on optimal control problem

1. Aug 22, 2011

Hi guys, I could use some help on the proof of a verification theorem for the following optimal control problem

$J_{M}(x;u)&\equiv&\mathbb{E}^{x}\left[\int_{0}^{\tau_{C}}\left(\int_{0}^{t}e^{-rs}\pi_{M}(x_{s})ds\right)\lambda u_{t}e^{-\lambda\int_{0}^{t}u_{z}dz}dt+\int_{0}^{\tau_{C}}\lambda u_{t}e^{-rt-\lambda\int_{0}^{t}u_{z}dz}\phi x_{t}dt\right]$

where the control can only assume the values 0 or 1.

Having some trouble with the standard verficication argument that relies on Dynkin Formula, since the limit of integration is a stopping time.

Last edited: Aug 22, 2011
2. Aug 22, 2011

### Staff: Mentor

Your equation does not seem to be rendering correctly for me. Does it appear okay in your browser? (I'm using IE)