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

Mathematics and finance: some philosophical remarks / Ippoliti, Emiliano. - In: TOPOI. - ISSN 1572-8749. - 40:4(2021), pp. 771-781. [10.1007/s11245-020-09706-1]

Mathematics and finance: some philosophical remarks

Emiliano Ippoliti
2021

Abstract

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
2021
mathematics; philosophy; finance; stock markets; ethics
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Mathematics and finance: some philosophical remarks / Ippoliti, Emiliano. - In: TOPOI. - ISSN 1572-8749. - 40:4(2021), pp. 771-781. [10.1007/s11245-020-09706-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1384554
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