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Stochastic Control Barrier Functions for Economics

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  • David van Wijk

Abstract

Control barrier functions (CBFs) and safety-critical control have seen a rapid increase in popularity in recent years, predominantly applied to systems in aerospace, robotics and neural network controllers. Control barrier functions can provide a computationally efficient method to monitor arbitrary primary controllers and enforce state constraints to ensure overall system safety. One area that has yet to take advantage of the benefits offered by CBFs is the field of finance and economics. This manuscript re-introduces three applications of traditional control to economics, and develops and implements CBFs for such problems. We consider the problem of optimal advertising for the deterministic and stochastic case and Merton's portfolio optimization problem. Numerical simulations are used to demonstrate the effectiveness of using traditional control solutions in tandem with CBFs and stochastic CBFs to solve such problems in the presence of state constraints.

Suggested Citation

  • David van Wijk, 2023. "Stochastic Control Barrier Functions for Economics," Papers 2312.12612, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2312.12612
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    1. Sethi, Suresh P. & Thompson, Gerald L., 1970. "Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 5(4-5), pages 381-394, December.
    2. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    3. M. L. Vidale & H. B. Wolfe, 1957. "An Operations-Research Study of Sales Response to Advertising," Operations Research, INFORMS, vol. 5(3), pages 370-381, June.
    4. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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