8731 10.4. Let X+ be an It diffusion on R and g: R R+ a continuous...

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8731 10.4. Let X+ be an It diffusion on R and g: R R+ a continuous reward function. Define 9(x) = sup{E*[g(X+)]; 7 stopping time, E* [7] < } . Show that g = g*. [Hint: If 7 is a stopping time put Tk = T^k for k = 1, 2, ... and consider Eg(X) X] E[_lim_g(X,k)]] 8731 10.4. Let X+ be an It diffusion on R and g: R R+ a continuous reward function. Define 9(x) = sup{E*[g(X+)]; 7 stopping time, E* [7] < } . Show that g = g*. [Hint: If 7 is a stopping time put Tk = T^k for k = 1, 2, ... and consider Eg(X) X] E[_lim_g(X,k)]]