IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_2539.html
   My bibliography  Save this paper

Application of Stochastic Optimal Control to Financial Market Debt Crises

Author

Listed:
  • Jerome L. Stein

Abstract

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis.

Suggested Citation

  • Jerome L. Stein, 2009. "Application of Stochastic Optimal Control to Financial Market Debt Crises," CESifo Working Paper Series 2539, CESifo.
    • Handle: RePEc:ces:ceswps:_2539
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp2539.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jerome L. Stein, 2005. "Optimal Debt And Endogenous Growth In Models Of International Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 389-413, December.
    2. Blanchet-Scalliet, Christophette & Diop, Awa & Gibson, Rajna & Talay, Denis & Tanre, Etienne, 2007. "Technical analysis compared to mathematical models based methods under parameters mis-specification," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1351-1373, May.
    3. Kristopher Gerardi & Andreas Lehnert & Shane M. Sherlund & Paul Willen, 2008. "Making Sense of the Subprime Crisis," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 39(2 (Fall)), pages 69-159.
    4. Fleming, Wendell H. & Stein, Jerome L., 2004. "Stochastic optimal control, international finance and debt," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 979-996, May.
    5. Stein, Jerome L., 2006. "Stochastic Optimal Control, International Finance, and Debt Crises," OUP Catalogue, Oxford University Press, number 9780199280575.
    6. Yuliya Demyanyk & Otto van Hemert, 2007. "Understanding the subprime mortgage crisis," Supervisory Policy Analysis Working Papers 2007-05, Federal Reserve Bank of St. Louis.
    7. Jerome L. Stein, 2003. "Stochastic Optimal Control Modeling of Debt Crises," CESifo Working Paper Series 1043, CESifo.
    8. Robert Jarrow, 2017. "Derivatives," World Scientific Book Chapters, in: THE ECONOMIC FOUNDATIONS OF RISK MANAGEMENT Theory, Practice, and Applications, chapter 3, pages 19-28, World Scientific Publishing Co. Pte. Ltd..
    9. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Haluk Yener & Thanasis Stengos & M. Ege Yazgan, 2017. "Analysis of the seeds of the debt crisis in Europe," The European Journal of Finance, Taylor & Francis Journals, vol. 23(15), pages 1589-1610, December.
    2. Adil NAAMANE, 2012. "Peut-on prévenir les crises financières ?," Working Papers 2011-2012_7, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised May 2012.
    3. Adil Naamane, 2012. "Peut-on prévenir les crises financières ?," Working Papers hal-01885154, HAL.

    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. Stein, Jerome L., 2010. "A tale of two debt crises: a stochastic optimal control analysis," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-24.
    2. Cheng, Mei-luan & Gloy, Brent A., 2008. "The Paradox of Risk Balancing: Do Risk-reducing Policies Lead to More Risk for Farmers?," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6546, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    3. Jerome L. Stein, 2010. "A Critique of the Literature on the US Financial Debt Crisis," CESifo Working Paper Series 2924, CESifo.
    4. Stein, Jerome L., 2010. "Alan Greenspan, the quants and stochastic optimal control," Economics Discussion Papers 2010-17, Kiel Institute for the World Economy (IfW Kiel).
    5. Stein, Jerome L., 2007. "United States current account deficits: A stochastic optimal control analysis," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1321-1350, May.
    6. Stein Jerome L., 2011. "US Financial Debt Crisis: A Stochastic Optimal Control Approach," Review of Economics, De Gruyter, vol. 62(3), pages 197-217, December.
    7. Jerome L. Stein, 2010. "Greenspan, Dodd-Frank and Stochastic Optimal Control," CESifo Forum, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 11(04), pages 55-62, December.
    8. Jerome L. Stein, 2010. "Greenspan's Retrospective of Financial Crisis and Stochastic Optimal Control," European Financial Management, European Financial Management Association, vol. 16(5), pages 858-871, November.
    9. Haluk Yener & Thanasis Stengos & M. Ege Yazgan, 2015. "Survival Maximizing Leverage of an Economy: The Case of Greece," Working Paper series 15-17, Rimini Centre for Economic Analysis.
    10. Haluk Yener & Thanasis Stengos & M. Ege Yazgan, 2017. "Analysis of the seeds of the debt crisis in Europe," The European Journal of Finance, Taylor & Francis Journals, vol. 23(15), pages 1589-1610, December.
    11. Serge Rey, 2009. "Des insuffisances de la PPA à l’apport du NATREX : une revue critique des théories du taux de change réel d’équilibre," Working Papers hal-01880363, HAL.
    12. Stein, Jerome L., 2011. "The crisis, Fed, Quants and stochastic optimal control," Economic Modelling, Elsevier, vol. 28(1-2), pages 272-280, January.
    13. Rey, Serge, 2009. "L’apport du NATREX à la modélisation des taux de change d’équilibre : théorie et application au dollar canadien," L'Actualité Economique, Société Canadienne de Science Economique, vol. 85(2), pages 131-181, juin.
    14. Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    15. Yener, Haluk & Soybilgen, Barış & Stengos, Thanasis, 2020. "A general model for financial crises: An application to eurozone crisis," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 202-229.
    16. Kelly, Robert & O'Toole, Conor, 2016. "Lending Conditions and Loan Default: What Can We Learn From UK Buy-to-Let Loans?," Research Technical Papers 04/RT/16, Central Bank of Ireland.
    17. Deniz Igan & Prachi Mishra & Thierry Tressel, 2012. "A Fistful of Dollars: Lobbying and the Financial Crisis," NBER Macroeconomics Annual, University of Chicago Press, vol. 26(1), pages 195-230.
    18. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    19. Gunther Capelle-Blancard, 2010. "Are Derivatives Dangerous? A Literature Survey," International Economics, CEPII research center, issue 123, pages 67-89.
    20. Bernanke, B.S., 2011. "International capital flows and the returns to safe assets in the United States 2003-2007," Financial Stability Review, Banque de France, issue 15, pages 13-26, February.

    More about this item

    Keywords

    stochastic optimal control; dynamic optimization; mortgage crisis; Ito equation; risk aversion; debt management; warning signals;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

    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:ces:ceswps:_2539. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.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.