IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v26y2022i1d10.1007_s00780-021-00469-0.html
   My bibliography  Save this article

The influence of economic research on financial mathematics: Evidence from the last 25 years

Author

Listed:
  • René Carmona

    (Princeton University)

Abstract

This is an attempt to review some of the breakthroughs in economic research as they impacted the nascent field of financial mathematics over the last 25 years. Because of the prominent role of Finance and Stochastics in the definition of this emerging field, I try to view things through the lens of its published papers, and I try to stay away from financial engineering applications.

Suggested Citation

  • René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:1:d:10.1007_s00780-021-00469-0
    DOI: 10.1007/s00780-021-00469-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-021-00469-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-021-00469-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hart, Oliver D & Moore, John, 1988. "Incomplete Contracts and Renegotiation," Econometrica, Econometric Society, vol. 56(4), pages 755-785, July.
    2. Thierry Jeantheau, 2004. "A link between complete models with stochastic volatility and ARCH models," Finance and Stochastics, Springer, vol. 8(1), pages 111-131, January.
    3. Oliver Hart & John Moore, 2008. "Contracts as Reference Points," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 1-48.
    4. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    5. Jean-Charles Rochet & Xavier Vives, 2004. "Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All?," Journal of the European Economic Association, MIT Press, vol. 2(6), pages 1116-1147, December.
    6. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    7. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    9. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    10. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    11. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    12. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    13. Holmstrom, Bengt & Milgrom, Paul, 1991. "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 7(0), pages 24-52, Special I.
    14. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    15. Christoph Kühn & Alexander Molitor, 2019. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 23(4), pages 1049-1077, October.
    16. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    17. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(4), pages 537-542.
    18. James A. Mirrlees, 1976. "The Optimal Structure of Incentives and Authority Within an Organization," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 105-131, Spring.
    19. Markus K. Brunnermeier & Yuliy Sannikov, 2016. "On the Optimal Inflation Rate," American Economic Review, American Economic Association, vol. 106(5), pages 484-489, May.
    20. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    21. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    22. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    23. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    24. Ernst Fehr & Oliver Hart & Christian Zehnder, 2011. "Contracts as Reference Points--Experimental Evidence," American Economic Review, American Economic Association, vol. 101(2), pages 493-525, April.
    25. Jean-Paul Décamps & Stéphane Villeneuve, 2019. "A two-dimensional control problem arising from dynamic contracting theory," Finance and Stochastics, Springer, vol. 23(1), pages 1-28, January.
    26. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    27. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    28. Vicky Henderson & Jonathan Muscat, 2020. "Partial liquidation under reference-dependent preferences," Finance and Stochastics, Springer, vol. 24(2), pages 335-357, April.
    29. Christoph Kuhn & Alexander Molitor, 2018. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Papers 1811.11621, arXiv.org, revised Apr 2019.
    30. Ernst Fehr & Oliver Hart & Christian Zehnder, 2008. "Contracts as reference points � experimental evidence," IEW - Working Papers 393, Institute for Empirical Research in Economics - University of Zurich.
    31. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    32. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    33. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    34. Bueler, Benno, 1997. "Solving an equilibrium model for trade of CO2 emission permits," European Journal of Operational Research, Elsevier, vol. 102(2), pages 393-403, October.
    35. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    36. Robert Fernholz, 2001. "Equity portfolios generated by functions of ranked market weights," Finance and Stochastics, Springer, vol. 5(4), pages 469-486.
    37. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    38. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    39. 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.
    40. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    41. repec:dau:papers:123456789/2267 is not listed on IDEAS
    42. John Kambhu & Neel Krishnan & Scott Weidman, 2007. "New directions for understanding systemic risk: a report on a conference cosponsored by the Federal Reserve Bank of New York and the National Academy of Sciences," Economic Policy Review, Federal Reserve Bank of New York, vol. 13(Nov), pages -83.
    43. Mikhail Golosov & John Hassler & Per Krusell & Aleh Tsyvinski, 2014. "Optimal Taxes on Fossil Fuel in General Equilibrium," Econometrica, Econometric Society, vol. 82(1), pages 41-88, January.
    44. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    45. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    46. René Carmona & Peiqi Wang, 2021. "A Probabilistic Approach to Extended Finite State Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 471-502, May.
    47. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    4. repec:dau:papers:123456789/5374 is not listed on IDEAS
    5. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    6. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, August.
    7. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    8. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    9. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    10. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    11. Marc Atlan & Hélyette Geman & Dilip Madan & Marc Yor, 2007. "Correlation and the pricing of risks," Annals of Finance, Springer, vol. 3(4), pages 411-453, October.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    13. Mykland, Per Aslak, 2019. "Combining statistical intervals and market prices: The worst case state price distribution," Journal of Econometrics, Elsevier, vol. 212(1), pages 272-285.
    14. John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 181-200.
    15. Müller, Daniel & Schmitz, Patrick W., 2016. "Vertragstheorie: Zum Nobelpreis 2016 für Oliver Hart und Bengt Holmström [Contract Theory: On the Contributions of the 2016 Nobel Laureates Oliver Hart and Bengt Holmström]," MPRA Paper 75233, University Library of Munich, Germany.
    16. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    17. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    18. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    19. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    20. Tompkins, Robert G. & D'Ecclesia, Rita L., 2006. "Unconditional return disturbances: A non-parametric simulation approach," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 287-314, January.
    21. Stijn Claessens & M Ayhan Kose, 2018. "Frontiers of macrofinancial linkages," BIS Papers, Bank for International Settlements, number 95.

    More about this item

    Keywords

    Financial mathematics; Economic research; Nobel prize;
    All these keywords.

    JEL classification:

    • B26 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Financial Economics
    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods
    • N20 - Economic History - - Financial Markets and Institutions - - - General, International, or Comparative

    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:spr:finsto:v:26:y:2022:i:1:d:10.1007_s00780-021-00469-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.