×

Time-discretization for controlled Markov processes. II: A jump and diffusion application. (English) Zbl 0874.93095

The authors apply their convergence theorem of Part I [ibid. 32, No. 1, 1-16 (1996), reviewed above] to two controlled Markov processes: to a controlled infinite server queue, and to a controlled cash-balance model. They obtain some computational schemes to approximate the optimal cost function and to construct an \(\varepsilon\)-optimal control.

MSC:

93E20 Optimal stochastic control
93C57 Sampled-data control/observation systems

Citations:

Zbl 0875.93056
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[1] A. Bensoussan M. Robin: On the convergence of the discrete time dynamic programming equation for general groups. SIAM J. Control Optim. 20 (1982), 1, 722-746. · Zbl 0488.93062 · doi:10.1137/0320053
[2] N. Christopeit: Discrete approximation of continuous time stochastic control systems. SIAM J. Control Optim. 21 (1983), 1, 17-40. · Zbl 0508.93065 · doi:10.1137/0321002
[3] G. M. Constantinides: Stochastic cash management with fixed and proportional transaction costs. Management Sci. 22 (1974), 1320-1331. · Zbl 0343.90021 · doi:10.1287/mnsc.22.12.1320
[4] G. M. Constantinides S. F. Richard: Existence of optimal simple policies for discounted-costs inventory and cash management in continuous time. Oper. Res. 26 (1978), 620-636. · Zbl 0385.90041 · doi:10.1287/opre.26.4.620
[5] B. T. Doshi: Optimal control of the service rate in an \(M|G|1\)-queueing system. Adv. in Appl. Probab. 10 (1978), 862-701. · Zbl 0381.60086 · doi:10.2307/1426641
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.