- #1
psalgado
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Hi guys, I could use some help on the proof of a verification theorem for the following optimal control problem
[itex] 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][/itex]
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.
[itex] 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][/itex]
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.
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