Topoi 40 (4):771-781 (2020)

Emiliano Ippoliti
Università degli Studi di Roma La Sapienza
I examine the role that mathematics plays in understanding and modelling finance, especially stock markets, and how philosophy affects it. To this end, I explore how mathematics penetrates finance via physics, constructing a ‘financial physics’, and I outline the philosophical backgrounds of this process, in particular the ‘philosophy of equilibrium’ and that of critical points or ‘out-of-equilibrium’. I discuss the main characteristics and a few weaknesses of these mathematizations of financial systems, notably econometrics and econophysics, and I compare the two ways, top-down and bottom-up, of building mathematical approaches to finance. The top-down approach is the most used and the most conservative. I argue that it guarantees a mathematical account, but it is less effective than the more difficult bottom-up approach, which is more appropriate and which may end up without a mathematical account of financial phenomena. I then consider two important issues raised by a mathematical approach to finance, that is, the performative and the reversing side of mathematics, and an ethics of mathematics. In the first case I argue that mathematics not only can be a performative device, but it also enables ‘reversing’ dynamics, that is, a mathematical model may become not a representational tool, but a device of social engineering—a mathematical way of investigating what are the initial conditions and processes needed to obtain an intended result. In the second case I argue that this specific relation between mathematical modelling and prediction raises an ethical question in finance, namely, a responsible construction and use of the mathematical models provided by a financial physics.1.From physics to finance: the mathematical way2.Finance, mathematics and the philosophy of equilibrium3.Finance, mathematics and critical points4.A mathematical access key?5.Performativity: the mathematical forging of finance6.An Ethics of mathematics in finance.
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DOI 10.1007/s11245-020-09706-1
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Essays in Positive Economics.Milton Friedman - 1953 - University of Chicago Press.
Credible Worlds: The Status of Theoretical Models in Economics.Robert Sugden - 2000 - Journal of Economic Methodology 7 (1):1-31.

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