垄断企业动态模型中的最优生产和定价策略
Optimal production and pricing strategies in a dynamic model of monopolistic firm
摘要：
考虑了垄断厂商的确定性连续时间模型，该模型选择单一产品的生产和定价策略。企业的目标是在无限时间范围内最大化贴现利润。无拖后假设引入了对库存量的状态约束。收入和生产费用函数假设是连续的，但一般来说，我们不强加的凸性/凸性属性。利用黏性解理论和Young-Fenchel对偶理论的结果，导出了值函数的一种表示，研究了它的正则性，并给出了这类非凸最优控制问题的最优策略的完整描述.与Chazal等人（2003）的结果一致，在有限时间内清算初始库存，然后使用最优静态策略是最优的。我们给出了一个条件，允许区分这种静态策略是否可以由普通或放松控制来表示。后者与生产周期有关。一般的理论是通过一个非凸生产成本的例子来说明的，这个例子是由Arvan和Moses（1981）提出的。
英文摘要：
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging assumption induces the state constraint on the inventory level. The revenue and production cost functions are assumed to be continuous but, in general, we do not impose the concavity/convexity property. Using the results form the theory of viscosity solutions and Young-Fenchel duality, we derive a representation for the value function, study its regularity properties, and give a complete description of optimal strategies for this non-convex optimal control problem. In agreement with the results of Chazal et al. (2003), it is optimal to liquidate initial inventory in finite time and then use an optimal static strategy. We give a condition, allowing to distinguish if this static strategy can be represented by an ordinary or relaxed control. The latter is related to production cycles. General theory is illustrate by the example of a non-convex production cost, proposed by Arvan and Moses (1981).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
