Extract
[...] Mathematically, we can pose: v_n = v_0 * a geometric sequence with a common ratio q and a first term v_0. If v_0 is the first wealth declared by a taxpayer, then any evolution of v_n that is not consistent with it must be verified by the tax administration. Suppose that the common ratio of our geometric sequence, is 1.1 (which corresponds to a 10% increase in wealth per year), any value of v_1 greater than 1.1 * v_0 should be considered suspicious. [...]
[...] The realization of these events does not always correspond to fraud. For example, it is possible to have inherited one's main residence and be, at the same time, registered in the France Work files, as an insured unemployed person. It is also possible to be domiciled in France and receive income from abroad: this is the case of border workers living near Switzerland, Luxembourg, or Belgium. However, a first sorting of these events based on probabilities could facilitate the work of the tax administration by bringing up a certain number of potentially suspicious cases. [...]
[...] In conclusion, we can say that mathematics and, more particularly, the tools related to geometric sequences, logarithmic functions, and probability theory play a crucial role in the fight against tax fraud and money laundering. These phenomena, in fact, represent real scourges for our contemporary societies. The mathematical tools we have presented during this grand oral offer the tax administration an arsenal to detect anomalies, identify suspicious behaviors, and uncover fraudulent networks. [...]
[...] To what extent do mathematics allow for the detection of tax fraud and money laundering? - Baccalaureate oral exam 5,800 billion euros: This is the estimate produced by French economist Gabriel Zucman of the astronomical amount of fortunes placed in the world's tax havens. It testifies to the scale of tax evasion, a phenomenon understood as the illegal avoidance of tax obtained by relocating part of one's assets abroad, even if the latter remains, by definition, difficult to estimate. It is very concretely about sums of money placed in countries such as Panama, Switzerland, or the British Virgin Islands, which, by definition, escape the tax systems of the countries where the fraudsters reside. [...]
[...] Firstly, the percentage change in wealth can be modified very easily according to the evolution of the economic situation. Secondly, the tax administration will be able to detect anomalies in taxpayers' declarations even after several years. Suppose, for example, that 5 years have passed: we will then have v_5 = v_0 * q^5. Logarithms are also useful for detecting tax fraud and money laundering. They allow, in fact, to compress the differences and accentuate certain statistical anomalies. This comes directly from the mathematical properties of logarithmic functions. These can be written in the form: = ln(x) + k. [...]
