# Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Neoclassical Financial Risk Modelling: “We Were Wrong”

#### 2.1. The Formula That Killed Wall Street

- −
- (Sarah Robertson) It’s legit… the kid killed it. The formula’s worthless.
- −
- (Jared Cohen) What does that mean?
- −
- (Sarah Robertson) It’s broken.
- −
- (Jared Cohen) There are 8 trillion dollars of paper around the world relying on that equation!
- −
- (Sarah Robertson) Well, we were wrong.

#### 2.2. The Performativity of Financial Risk Modelling: Dispositive and Discourse

#### 2.2.1. Socio-Technical Instruments: The Financialised Tools

#### 2.2.2. Discourse of Financialisation: The Financial Logos

#### 2.3. Sustainable Finance and Epistemic Ethics

## 3. From the Philosophy of Science to the Risk Culture in Finance

#### 3.1. Mental Models in Finance

#### 3.2. The Philosophy Hook: The Principle of Continuity and the Theory of Average

#### 3.3. From Philosophy to Mental Model of Financial Techniques: The Risk Culture of Finance

#### 3.4. Sustainable Risk Culture for Financial Risk Modelling

## 4. The Unsustainable Risk Culture of Brownian Finance and Its Cognitive Biases

#### 4.1. Brownian Regulation and Financial Black Swans

#### 4.2. The Status of Discontinuities in Brownian Risk Culture

#### 4.3. A Note from Keynes

## 5. A Possible Solution for the Sustainable Modelling of Financial Risk: Fractal Geometry

#### 5.1. Is Fractal Geometry a “Sustainable” Geometry of Nature?

#### 5.1.1. Fractals in Nature

#### 5.1.2. Fractals and Sustainability

#### 5.2. Fractalisation of Financial Risk Modelling

#### 5.2.1. The Greening of Financial Risk Models and the Green Premium Puzzles

#### 5.2.2. How to Reconcile Finance and Nature

## 6. Conclusions and Future Research

- (1)
- To verify how good are fractal and multifractal methods to model important features of physical and human geographies in the sense of SDGs.
- (2)
- If a relevant financial risk modelling should take these fractal characteristics into account, to seek to construct “green metrics” and tools in the fractal sense to lay the groundwork for ecological finance theory as an alternative of neoclassical finance.
- (3)
- To apply these new metrics to portfolio management and risk measurement techniques.
- (4)
- To introduce financial risk modelling issues and metrics into a philosophical reflection on epistemic ethics because financial tools and financial risk modelling contribute to shape the real world. This last issue is important, keeping in mind that ecological finance theory aims to move from “what is” to “what should be”.

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Pareto Distributions, Scaling Laws and Irregularity

^{−α}. If the scale invariance property is validated, objects do not change if scales of length are multiplied by a common factor. It represents a kind of universality. Like Russian dolls, the shape of the object repeats itself at all sizes. It is said that there is a self-similarity of the phenomenon being studied. So there is a relationship between power law and self-similarity. Here again, in practice, there are several forms of self-similarity, but we do not want to complicate the presentation in the context of this introductory article.

^{α}for x > a. We find a power law. The name of this function comes from the fact that one of the quantities (here, the cumulative empirical frequency) varies as the power of another (here, the values exceeding the threshold). This is the Pareto type I distribution. A very large number of situations are possible, especially with other power laws, but we do not intend to make the presentation more complicated here. Turning now to the empirical data and empirical frequencies, a rank-frequency diagram allows us to visually capture a characteristic property of Pareto’s power laws. The straight line of the log-log plot has the slope −α. In fact, when logarithms are taken instead of raw values, if $Y=a{X}^{-\alpha}$, then ln Y = −α lnX + k. We deduce from this that the “signature” of a power law is a linear relationship between the two quantities in log-log diagram.

## Appendix B

#### Fractal Properties of Neoclassical Finance Theory and Beyond

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Walter, C. Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections. *Sustainability* **2020**, *12*, 7789.
https://doi.org/10.3390/su12187789

**AMA Style**

Walter C. Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections. *Sustainability*. 2020; 12(18):7789.
https://doi.org/10.3390/su12187789

**Chicago/Turabian Style**

Walter, Christian. 2020. "Sustainable Financial Risk Modelling Fitting the SDGs: Some Reflections" *Sustainability* 12, no. 18: 7789.
https://doi.org/10.3390/su12187789