Optimal Spatial Pricing Strategies With A Stochastic Factor

Asset pricing problem has always been a hot and difficult problem in the field of financial research.Especially,commodity pricing problems sometimes involve the role of spatial and temporal factors.The classical pricing problems of agent usually focus on the situation of certain consumption location.However,in the real world,uncertainty is universal.Therefore,this paper intends to consider the pricing problem of agent under the condition of uncertain consumption location.In this paper,we study the optimal consumption problem of consumers with stochastic consumption location,and the optimal pricing problem of the agent.Firstly,we study the stochastic optimal consumption problem of consumers,that is,finding the optimal consumption strategies which minimize the total expenditure.By using the maximum principle and finite covering principle,we obtain the existence and consistency results of the optimal consumption strategies under the weak topology.Secondly,we study the optimal pricing problem of the agent.By introducing the expected c-concave function,combined with the existence of optimal consumption strategies,the optimal pricing problem of the agent is transformed into a new optimization problem which based on the expected c-concave function family.Furthermore,by using the Weierstrass optimization principle,we can obtain the existence result of the optimal pricing problem.The study of this paper can be regarded as a natural generalization of the classic deterministic space pricing problem.