Optimal control of dynamic investment on inventory with stochastic demand

Based on mean-variance criterion and stochastic quadratic-linear optimal control theory, A dynamic model about portfolio of economic production-inventory investment control is formulated with stochastic demand in this paper. The objective is to maximize the expected terminal return and minimize the cost and variance of the terminal wealth. We studies a method to obtain the optimal solution: by solving the corresponding stochastic-Jacobian-Bellman equation of this model. Finally, An example is given to demonstrate the best investment and production strategies obtained from the model.