Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity solution of the transformed Hamilton-Jacobi-Bellman equation associated with this model. Finally, the optimal consumption policy is derived from the optimality conditions in the HJB equation.