Optimal consumption of the stochastic Ramsey problem for non-Lipschitz diffusion

[摘要] The stochastic Ramsey problem is considered in a growth model with the production function of a Cobb-Douglas form. The existence of a unique classical solution is proved for the Hamilton-Jacobi-Bellman equation associated with the optimization problem. A synthesis of the optimal consumption policy in terms of its solution is proposed. MSC:49L20, 49L25, 91B62.

[学科分类] 数学（综合）

[关键词] Hamilton-Jacobi-Bellman equation;viscosity solutions;Ramsey problem;Cobb-Douglas production function