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Optimal Management of Groundwater Under Uncertainty: A Unified Approach

机译：不确定性下的地下水优化管理：统一方法

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Discrete-time stochastic models of management of groundwater resources have been extensively used for understanding a number of issues in groundwater management. Most models used suffer from two drawbacks: relatively simplistic treatment of the cost of water extraction, and a lack of important structural results (such as monotonicity of extraction in stock and concavity of the value function), even in simple models. Lack of structural properties impede both practical policy simulation and clarity of understanding of the resulting models and the underlying economics. This paper provides a unifying framework for these models in two directions; first, the usual cost function is extended to encompass cases where marginal cost of pumping depends on the stock and second, the analysis dispenses with assumptions of concavity of the objective function and compactness of the state space, using instead lattice-theoretic methods. With these modifications, a comprehensive investigation of which structural properties can be proved in each of the resulting cases is carried out. It is shown that for some of the richer models more structural properties may be proved than for the simpler model used in the literature. This paper also introduces to the resource economics literature an important method of proving convergence to a stationary distribution which does not require monotonicity in stock of resource. This method is of interest in a variety of renewable resource model settings.
机译：地下水资源管理的离散时间随机模型已广泛用于理解地下水管理中的许多问题。所使用的大多数模型都具有两个缺点：即使是简单的模型，水提取成本的处理也相对简单，并且缺乏重要的结构结果（例如库存中的单调性和价值函数的凹度）。缺乏结构特性既阻碍了实际的政策模拟，也阻碍了对所得模型和基本经济学的理解。本文为两个模型提供了一个统一的框架。首先，通常的成本函数被扩展到包括边际抽水成本取决于存货的情况；其次，该分析无需使用目标函数的凹性和状​​态空间紧凑性的假设，而是采用格理论方法。通过这些修改，可以对每种情况下可证明哪些结构性能进行全面研究。结果表明，对于某些更丰富的模型，与文献中使用的简单模型相比，可以证明更多的结构特性。本文还向资源经济学文献介绍了一种证明收敛到平稳分布的重要方法，该平稳分布不需要资源存量的单调性。这种方法在各种可再生资源模型设置中都很有趣。

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