IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/1903.html
   My bibliography  Save this paper

On the universal method to solve extremal problems

Author

Listed:
  • Brinkhuis, J.

Abstract

Some applications of the theory of extremal problems to mathematics and economics are made more accessible to non-experts. 1.The following fundamental results are known to all users of mathematical techniques, such as economist, econometricians, engineers and ecologists: the fundamental theorem of algebra, the Lagrange multiplier rule, the implicit function theorem, separation theorems for convex sets, orthogonal diagonalization of symmetric matrices. However, full explanations, including rigorous proofs, are only given in relatively advanced courses for mathematicians. Here, we offer short ans easy proofs. We show that akk these results can be reduced to the task os solving a suitable extremal problem. Then we solve each of the resulting problems by a universal strategy. 2. The following three practical results, each earning their discoverers the Nobel prize for Economics, are known to all economists and aonometricians: Nash bargaining, the formula of Black and Scholes for the price of options and the models of Prescott and Kydland on the value of commitment. However, the great value of such applications of the theory of extremal problems deserves to be more generally appreciated. The great impact of these results on real life examples is explained. This, rather than mathematical depth, is the correct criterion for assessing their value.

Suggested Citation

  • Brinkhuis, J., 2005. "On the universal method to solve extremal problems," Econometric Institute Research Papers EI 2005-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1903
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/1903/ei200502.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    2. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678, arXiv.org.
    2. Zhang, Cathy, 2014. "An information-based theory of international currency," Journal of International Economics, Elsevier, vol. 93(2), pages 286-301.
    3. Heller, Yuval & Peleg Lazar, Sharon & Raviv, Alon, 2022. "Banks’ risk taking and creditors’ bargaining power," Journal of Corporate Finance, Elsevier, vol. 74(C).
    4. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    5. Mordecai Avriel & Jens Hilscher & Alon Raviv, 2013. "Inflation Derivatives Under Inflation Target Regimes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(10), pages 911-938, October.
    6. Völz, Manja & Wedow, Michael, 2009. "Does banks size distort market prices? Evidence for too-big-to-fail in the CDS market," Discussion Paper Series 2: Banking and Financial Studies 2009,06, Deutsche Bundesbank.
    7. Brendon, Charles & Ellison, Martin, 2018. "Time-consistently undominated policies," LSE Research Online Documents on Economics 87176, London School of Economics and Political Science, LSE Library.
    8. Alex Garivaltis, 2019. "Nash Bargaining Over Margin Loans to Kelly Gamblers," Risks, MDPI, vol. 7(3), pages 1-14, August.
    9. Vincent P. Crawford, 1985. "Dynamic Games and Dynamic Contract Theory," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(2), pages 195-224, June.
    10. Ali Hussein Samadi & Afshin Montakhab & Hussein Marzban & Sakine Owjimehr, 2017. "Quantum Barro--Gordon Game in Monetary Economics," Papers 1708.05689, arXiv.org.
    11. Oliver Hart & Luigi Zingales, 2011. "A New Capital Regulation for Large Financial Institutions," American Law and Economics Review, American Law and Economics Association, vol. 13(2), pages 453-490.
    12. Douven, R.C.M.H., 1995. "Policy coordination and convergence in the EU," Other publications TiSEM d4354b51-1c72-4109-9bde-e, Tilburg University, School of Economics and Management.
    13. Tumellano Sebehela, 2017. "Game Options," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 1-17, September.
    14. Alex Garivaltis, 2019. "The Laws of Motion of the Broker Call Rate in the United States," IJFS, MDPI, vol. 7(4), pages 1-23, October.
    15. Hsieh Hsih-chia & Hsieh Pei-gin, 2004. "A Generalized Theory of Monetary and Macroeconomics," Money Macro and Finance (MMF) Research Group Conference 2004 50, Money Macro and Finance Research Group.
    16. Samadi, Ali Hussein & Montakhab, Afshin & Marzban, Hussein & Owjimehr, Sakine, 2018. "Quantum Barro–Gordon game in monetary economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 94-101.
    17. Suresh P. Sethi & Sushil Gupta & Vipin K. Agrawal & Vijay K. Agrawal, 2022. "Nobel laureates’ contributions to and impacts on operations management," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4283-4303, December.
    18. Lorán Chollete & Sharon G. Harrison, 2021. "Unintended Consequences: Ambiguity Neglect and Policy Ineffectiveness," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 47(2), pages 206-226, April.
    19. van der Ploeg, F. & Markink, A.J., 1991. "Dynamic policy in linear models with rational expectations of future events : A computer package," Other publications TiSEM 3acd93c9-b28d-4acb-a750-c, Tilburg University, School of Economics and Management.
    20. Völz, Manja & Wedow, Michael, 2011. "Market discipline and too-big-to-fail in the CDS market: Does banks' size reduce market discipline?," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 195-210, March.

    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:ems:eureir:1903. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.