Question: 11.7.* Consider the stochastic control problem (system) dXt = au(t)dt + u(t)dBt ; X0 = x > 0 where Bt R, u(t) R and a

11.7.* Consider the stochastic control problem (system) dXt = au(t)dt + u(t)dBt ; X0 = x > 0 where Bt R, u(t) R and a R is a given constant, and (performance) (s, x) = sup u Es,x[(X )] , where 0 0;Xt = 0} (T s) , T being a given future time (constant). Show that this problem has the optimal control u (t, x) = ax 1 with corresponding optimal performance (s, x) = x expa2(T s) 2(1 )

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