IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2312.12612.html
   My bibliography  Save this paper

Stochastic Control Barrier Functions for Economics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2312.12612
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. An, Jongbong & Jeon, Junkee & Kim, Takwon, 2025. "Optimal portfolio and retirement decisions with costly job switching options," Applied Mathematics and Computation, Elsevier, vol. 491(C).
    2. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    3. Hong, Claire Yurong & Lu, Xiaomeng & Pan, Jun, 2021. "FinTech adoption and household risk-taking," BOFIT Discussion Papers 14/2021, Bank of Finland Institute for Emerging Economies (BOFIT).
    4. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    5. Auffret, Philippe, 2001. "An alternative unifying measure of welfare gains from risk-sharing," Policy Research Working Paper Series 2676, The World Bank.
    6. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    7. Chen, An & Hieber, Peter & Sureth, Caren, 2022. "Pay for tax certainty? Advance tax rulings for risky investment under multi-dimensional tax uncertainty," arqus Discussion Papers in Quantitative Tax Research 273, arqus - Arbeitskreis Quantitative Steuerlehre.
    8. Mayank Goel & Suresh Kumar K., 2006. "A Risk-Sensitive Portfolio Optimisation Problem with Stochastic Interest Rate," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 5(3), pages 263-282, December.
    9. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    10. John H. Cochrane, 1999. "New facts in finance," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 23(Q III), pages 36-58.
    11. Mr. Christopher Carroll & Mr. Martin Sommer & Mr. Jiri Slacalek, 2012. "Dissecting Saving Dynamics: Measuring Wealth, Precautionary, and Credit Effects," IMF Working Papers 2012/219, International Monetary Fund.
    12. Montserrat Guillén & Jean Pinquet, 2008. "Long-Term Care: Risk Description of a Spanish Portfolio and Economic Analysis of the Timing of Insurance Purchase," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(4), pages 659-672, October.
    13. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    14. John Y. Campbell & Luis M. Viceira & Joshua S. White, 2003. "Foreign Currency for Long-Term Investors," Economic Journal, Royal Economic Society, vol. 113(486), pages 1-25, March.
    15. Stephen Satchell & Susan Thorp, 2007. "Scenario Analysis with Recursive Utility: Dynamic Consumption Plans for Charitable Endowments," Research Paper Series 209, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    17. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    18. Zongxia Liang & Xiaodong Luo & Fengyi Yuan, 2023. "Consumption-investment decisions with endogenous reference point and drawdown constraint," Mathematics and Financial Economics, Springer, volume 17, number 6, September.
    19. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    20. Jorge Braga de Macedo & Jeffrey Goldstein & David Meerschwam, 1984. "International Portfolio Diversification: Short-Term Financial Assets and Gold," NBER Chapters, in: Exchange Rate Theory and Practice, pages 199-238, National Bureau of Economic Research, Inc.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2312.12612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.