Ricerc@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, responsible construction and use of the mathematical models provided by a financial physics.

1. From physics to finance: the mathematical way
2. Finance, mathematics and the philosophy of equilibrium
3. Finance, mathematics and critical points
4. A mathematical access key?
5. Performativity: the mathematical forging of finance
6. An Ethics of mathematics in finance