An investor's wealth dynamics is given by the following: Xt+1= UfWt where {w} is an i.i.d. positive, R-valued, stochastic process. The investor has access to the past and current wealth information and his actions. The goal is to maximize: J(xo; II) = T-1 Erolb(x- ut)] t=0 The investor's action set for any given x is: U(x) = [0, x]. Formulate the problem as an optimal stochastic control problem by clearly identifying the state, the control actions, the information available at the controller, and the cost functional mapping the actions and states to R+. Derive the HJB equation for this problem.