An inventory system with stochastic environmental impacts: Production and pricing
报告人:卢相刚
报告地点:腾讯会议ID:679-387-167;会议密码:123456
报告时间:2022年11月15日星期二14:00-15:00
邀请人:李晓月
报告摘要:
This paper studies how a monopoly firm produces and prices its product under the influence of stochastic market environment and reference price. We formulate it as a stochastic control problem, whose aim is to maximize the net profit. The evolution of inventory system and reference price is given by a two-dimensional controlled stochastic differential equation, while the stochastic market environment is captured by a continuous time Markov chain. Firstly, by using the dynamic program principle and the viscosity solution method, we show that the value function is the unique viscosity solution to the associated optimization equation, also known as the Hamilton-Jacobi-Bellman (HJB) equation. Since the HJB equation is usually not easy to solve explicitly, we figure out the finite difference approximation scheme to numerically approximate the value function. Convergence analysis is also given. Finally, through numerical examples and sensitivity analysis, our theoretical research results are intuitively demonstrated, which provides a quantitative reference for inventory management in practice.
主讲人简介:
卢相刚,博士,广东工业大学数学与统计学院校聘副教授,硕士生导师,博士毕业于中山大学数学学院概率统计专业,师从郭先平教授,主要从事基于随机微分方程的优化控制、数值逼近算法及其在金融保险等领域应用的相关问题的研究工作。目前的研究兴趣包括随机过程、随机分析、随机控制、随机优化在保险问题中的应用等。曾获国家自然科学基金青年基金项目一项,目前主持国家自然科学基金天元访问学者项目一项(与南开大学郭军义教授合作),广州市科技计划项目一项。