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.
Similar content being viewed by others
Notes
Throughout the paper, we use the short terminology Nobel prize in economics even though we should say The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.
References
Achdou, Y., Han, J., Lasry, J.M., Lions, P.L., Moll, B.: Income and wealth distribution in macroeconomics: A continuous-time approach (2017). Preprint. Available online at http://www.nber.org/papers/w23732
Aït-Sahalia, Y., Jacod, J.: High-Frequency Financial Econometrics. Princeton University Press, Princeton (2014)
Aiyagari, S.R.: Uninsured idiosyncratic risk and aggregate saving. Q. J. Econ. 109, 659–684 (1994)
Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203–228 (1999)
Black, F.: The pricing of commodity contracts. J. Financ. Econ. 3, 167–179 (1976)
Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 3, 637–654 (1973)
Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. J. Econom. 31, 307–327 (1986)
Brunnermeier, M., Sannikov, Y.: On the optimal inflation rate. Am. Econ. Rev. 106, 484–489 (2016)
Brunnermeier, M., Sannikov, Y.: Macro, money and finance: A continuous time approach. In: Taylor, J.B., Uhlig, H. (eds.) Handbook of Macroeconomics, vol. 2, pp. 1497–1546. Elsevier, Amsterdam (2017)
Bueler, B.: Solving an equilibrium model for trade of \({\mathrm {CO}_{2}}\) emission permits. Eur. J. Oper. Res. 102, 393–403 (1997)
Campbell, J.Y., Lo, A.W., MacKinlay, A.C.: The Econometrics of Financial Markets. Princeton University Press, Princeton (1996)
Carmona, R.: Applications of mean field games in financial engineering and economic theory. In: Delarue, F. (ed.) AMS Short Course on Mean Field Games, pp. 165–220. Am. Math. Soc., Providence RI (2022)
Carmona, R., Delarue, F.: Probabilistic Theory of Mean Field Games: Vol. I, Mean Field FBSDEs, Control, and Games. Springer, Berlin (2017)
Carmona, R., Fehr, M., Hinz, J., Porchet, A.: Market design for emissions markets trading schemes. SIAM Rev. 52, 403–452 (2010)
Carmona, R., Wang, P.: A probabilistic approach to extended finite state mean field games. Math. Oper. Res. 46, 471–502 (2021)
Carmona, R., Wang, P.: Finite-state contract theory with a principal and a field of agents. Manag. Sci. 67, 4725–4741 (2021)
Cox, J., Rubinstein, M.: Options Markets. Prentice Hall, New York (1985)
Cvitanić, J., Possamaï, D., Touzi, N.: Dynamic programming approach to principal–agent problems. Finance Stoch. 22, 1–37 (2018)
Cvitanić, J., Zhang, J.: Contract Theory in Continuous-Time Models. Springer, Berlin (2013)
Décamps, J.P., Villeneuve, S.: A two-dimensional control problem arising from dynamic contracting theory. Finance Stoch. 23, 1–28 (2019)
Diamond, D.W., Dybvig, P.H.: Bank runs, deposit insurance, and liquidity. J. Polit. Econ. 91, 401–419 (1983)
Duffie, D.: Dynamic Asset Pricing Theory. Princeton University Press, Princeton (1992)
Duffie, D., Gârleanu, N.: Risk and valuation of collateralized debt obligations. Financ. Anal. J. 57, 41–59 (2001)
Duffie, D., Pan, J.: An overview of value at risk. J. Deriv. 4, 7–49 (1997)
Duffie, D., Singleton, K.: Modeling term structures of defaultable bonds. Rev. Financ. Stud. 12, 687–720 (1999)
Elie, R., Mastrolia, T., Possamaï, D.: A tale of a principal and many, many agents. Math. Oper. Res. 44, 440–467 (2019)
Engle, R.F.: Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007 (1982)
Fernholz, R.: Equity portfolios generated by functions of ranked market weights. Finance Stoch. 5, 469–486 (2001)
Föllmer, H., Leukert, P.: Quantile hedging. Finance Stoch. 3, 251–273 (1999)
Fouque, J.P., Langsam, J.: Handbook on Systemic Risk. Cambridge University Press, Cambridge (2013)
Fouque, J.P., Papanicolaou, G., Sircar, R.: Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press, Cambridge (2000)
Fouque, J.P., Papanicolaou, G., Sircar, R., Solna, K.: Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives. Cambridge University Press, Cambridge (2011)
Golosov, M., Hassler, J., Krusell, P., Tsyvinski, A.: Optimal taxes on fossil fuel in general equilibrium. Econometrica 82, 41–88 (2014)
Granger, C.W.J.: The typical spectral shape of an economic variable. Econometrica 34, 150–161 (1966)
Harrison, J.M., Kreps, D.M.: Martingales and arbitrage in multiperiod security markets. J. Econ. Theory 20, 381–408 (1979)
Harrison, J.M., Pliska, S.: Martingales and stochastic integrals in the theory of continuous trading. Stoch. Process. Appl. 11, 215–260 (1981)
Hart, O., Grossman, S.: An analysis of the principal–agent problem. Econometrica 51, 7–46 (1983)
Hart, O., Moore, J.H.: Incomplete contracts and renegotiation. Econometrica 56, 1–48 (1988)
Hart, O., Moore, J.H.: Contracts as reference points. Q. J. Econ. 123, 1–48 (2008)
Haurie, A., Viguier, L.: A stochastic dynamic game of carbon emissions trading. Environ. Model. Assess. 8, 239–248 (2003)
Heath, D., Jarrow, R., Morton, A.: Bond pricing and the term structure of interest rates: A new methodology for contingent claim valuation. Econometrica 60, 77–105 (1992)
Henderson, V., Muscat, J.: Partial liquidation under reference-dependent preferences. Finance Stoch. 24, 335–357 (2020)
Holmström, B.: Moral hazard and observability. Bell J. Econ. 10, 74–91 (1979)
Holmström, B.: Moral hazard in teams. Bell J. Econ. 13, 324–340 (1982)
Holmström, B., Milgrom, P.: Aggregation and linearity in the provision of inter-temporal incentives. Econometrica 55, 303–328 (1987)
Holmström, B., Milgrom, P.: Multitask principal–agent analyses: Incentive contracts, asset ownership, and job design. J. Law Econ. Organ. 7, 24–52 (1991)
Jeantheau, T.: A link between complete models with stochastic volatility and ARCH models. Finance Stoch. 8, 111–131 (2004)
Kahneman, D., Tversky, A.: Prospect theory: An analysis of decision under risk. Econometrica 47, 263–291 (1979)
Kambhu, J., Weidman, S., Krishnan, N. (eds.): 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. National Research Council (2007). Available online at https://doi.org/10.17226/11914
Krusell, P., Smith, A. Jr.: Income and wealth heterogeneity in the macroeconomy. J. Polit. Econ. 106, 867–896 (1998)
Kühn, C., Molitor, A.: Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs. Finance Stoch. 23, 1049–1077 (2019)
Mao, T., Cai, J.: Risk measures based on the behavioural economics theory. Finance Stoch. 22, 367–393 (2018)
Markowitz, H.M.: Portfolio selection. J. Finance 7, 77–91 (1952)
Markowitz, H.M.: Mean–Variance Analysis in Portfolio Choice and Capital Markets. Basil Blackwell, Oxford (1987)
Merton, R.: An intertemporal capital asset pricing model. Econometrica 41, 867–887 (1973)
Merton, R.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4, 141–183 (1973)
Merton, R.: Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3, 125–144 (1976)
Mirrlees, J.: The optimal structure of incentives and authority within an organization. Bell J. Econ. 7, 105–131 (1976)
Morris, S., Shin, H.S.: Unique equilibrium in a model of self-fulfilling currency attacks. Am. Econ. Rev. 88, 587–597 (1998)
Pagès, G., Possamaï, D.: A mathematical treatment of bank monitoring incentives. Finance Stoch. 18, 39–73 (2014)
PERFORM: Performance-based energy resource feedback, optimization, and risk management (2020). Available online at https://arpa-e.energy.gov/technologies/programs/perform
Pliska, S.: A stochastic calculus model of continuous trading: Optimal portfolios. Math. Oper. Res. 11, 371–382 (1986)
Rochet, J.C., Vives, X.: Coordination failures and the lender of last resort. J. Eur. Econ. Assoc. 2, 1116–1148 (2004)
Samuelson, P.A.: The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Rev. Econ. Stud. 37, 537–542 (1970)
Samuelson, P.A., Dorfman, R., Solow, R.M.: Linear Programming and Economic Analysis. McGraw-Hill, New York (1958)
Sannikov, Y.: A continuous-time version of the principal–agent problem. Rev. Econ. Stud. 75, 957–984 (2008)
Sannikov, Y.: Contracts: The theory of dynamic principal–agent relationships and the continuous-time approach. In: Acemoglu, D. (ed.) Advances in Economics and Econometrics: Tenth World Congress, pp. 89–124. Cambridge University Press, Cambridge (2013)
von Neumann, J.: Zur Theorie der Gesellschaftsspiele. Math. Ann. 100, 295–320 (1928)
von Neumann, J.: On the theory of games of strategy. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games. 4, vol. 100, pp. 13–42 (1959)
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Acknowledgements
I want to personally thank Martin Schweizer for inviting me to contribute to this special issue, for accepting to let me write an opinion piece instead of a scientific review paper, and for patiently helping me turn my unstructured notes into a readable outcome.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A: List of Nobel laureates
Table 1 gives the recipients of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, an award which is abusively known as the Nobel in economics. We marked with an asterix those individuals cited in the text.
Appendix B: CME-MSRI prize medalists
Table 2 lists the recipients of the CME Group–MSRI Prize in Innovative Quantitative Applications. This medal is awarded to an individual or a group to recognise originality and innovation in the use of mathematical, statistical or computational methods for the study of the behaviour of markets, and more broadly of economics. As in the case of the Nobel prize, an asterisk identifies those individuals who are cited in the text. Since official citations were not available, in lieu of official reason for the award, I suggested a few words describing some of the reasons these academics are known in the financial mathematics community.
Rights and permissions
About this article
Cite this article
Carmona, R. The influence of economic research on financial mathematics: Evidence from the last 25 years. Finance Stoch 26, 85–101 (2022). https://doi.org/10.1007/s00780-021-00469-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00780-021-00469-0