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Stochastic Optimal Control

In: Optimal Control Theory

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  • Suresh P. Sethi

    (University of Texas at Dallas)

Abstract

When a dynamic system is subject to uncertainty, the state of the system is modeled as a stochastic process. In Sect. 12.1, we consider stochastic optimal control problems when the state equations are stochastic differential equations involving Wiener processes, known as Itô equations. Our goal will be to synthesize optimal feedback controls for such systems in a way that maximizes the expected value of a given objective function. In Sect. 12.2, we treat a stochastic production planning model in which the inventory is subject to uncertain disturbances such as sales returns and spoilage. We aim to obtain an optimal production policy that minimizes the expected total cost of inventories and backlogs over a finite horizon. In Sect. 12.3, we will solve an infinite-horizon optimal stochastic advertising problem with the sales-advertising dynamics is given by the Sethi advertising model explicitly. In Sect. 12.4, we formulate a classical consumption-investment problem. The objective is to find the optimal allocation of investment in risk-free and risky assets and consumption rate over time to maximize the discounted value of the utility of consumption over an infinite horizon. In Sect. 12.5, we will conclude the chapter by mentioning other types of stochastic optimal control problems that arise in practice. There are many exercises at the end of the chapter.

Suggested Citation

  • Suresh P. Sethi, 2021. "Stochastic Optimal Control," Springer Texts in Business and Economics, in: Optimal Control Theory, edition 4, chapter 12, pages 345-365, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-91745-6_12
    DOI: 10.1007/978-3-030-91745-6_12
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