后备技术不确定下资源耗竭动态优化模型研究

Study on dynamic optimal model of resource depletion under technological uncertainty

不确定性是资源耗竭理论的一个重要研究方向,资源替代研究中经常涉及技术不确定问题.在技术出现时间不确定问题描述的基础上,考虑资源开采成本与开采量相关以及有存货情形,利用动态规划思想处理了技术出现时间不确定,构建了动态优化模型,得到相应地HJB方程和最优开采路径.研究结果表明:确定性情形是不确定性的特例;在早期开采阶段,资源开采速度随着替代技术出现可能性提高而加快,开采了一段时间后,资源的开采速度随着替代技术出现可能性提高而减慢;关系转折时间点取决于资源初始储量,初始储量越大,该时间点越往后延长.

Uncertainty is one of the important research aspects. Technological uncertainty is often referred to when one studies in the field of resource substitute. By describing the case where the invention date is uncertain and considering the relation of extraction rate with extraction cost, the dynamic optimal model is built by using the idea of dynamic planning. HJB equation and optimal extraction path are found. The results show： the study of uncertainty often includes the situation of certainty; in the early stage of resource extraction, extraction rate of resources will increase with the probability of introduction of substitutable technology. But after a period of extraction, the case is reverse; the changing point of this relation is dependent on initial stock of resources. The larger the initial stock, the later the changing point of relation.