Schr\"odinger group and quantum finance

Juan M. Romero; Ulises Lavana; Elio Martínez

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arXiv · 1304.4995

Schr\"odinger group and quantum finance

Juan M. Romero·Ulises Lavana·Elio Martínez

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Abstract

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schr\"odinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schr\"odinger algebra representation is constructed.

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Juan M. Romero, Ulises Lavana, Elio Martínez. 2013-04-18. Schr\"odinger group and quantum finance. https://arxiv.org/abs/1304.4995

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