Optimal impulse control for a multidimensional cash management system with generalized cost functions
Optimal impulse control for a multidimensional cash management system with generalized cost functions
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DOI：
10.1016/j.ejor.2008.02.040
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发表时间：
2009-07-01
影响因子：
6.4
通讯作者：
Baccarin, Stefano
中科院分区：
文献类型：
--
作者：
Baccarin, Stefano
我们考虑多维现金管理系统的最优控制，其中现金余额波动为 R(n) 中的同质扩散过程。我们将该模型表述为具有无界成本函数的无界域上的脉冲控制问题。在一般假设下，我们将价值函数描述为加权 Sobolev 空间中拟变分不等式的弱解，并证明最优策略的存在。此外，我们证明了有限元方案的局部一致收敛性，以数值计算价值函数和最优成本。我们使用线性和距离成本函数计算二维模型的解，显示这两种简单情况下最优策略的形状。最后，我们的第三个数值实验计算了中央金库现金集中在两个银行账户的实际情况下的解决方案。 (C) 2008 Elsevier B.V. 保留所有权利。
We consider the optimal control of a multidimensional cash management system where the cash balances fluctuate as a homogeneous diffusion process in R(n). We formulate the model as an impulse control problem on an unbounded domain with unbounded cost functions. Under general assumptions we characterize the value function as a weak solution of a quasi-variational inequality in a weighted Sobolev space and we show the existence of an optimal policy. Moreover we prove the local uniform convergence of a finite element scheme to compute numerically the value function and the optimal cost. We compute the solution of the model in two-dimensions with linear and distance cost functions, showing what are the shapes of the optimal policies in these two simple cases. Finally our third numerical experiment computes the solution in the realistic case of the cash concentration of two bank accounts made by a centralized treasury. (C) 2008 Elsevier B.V. All rights reserved.