This paper is devoted to the connection between the probability distributions which produce solutions of the one-dimensional, time-independent Schr?dinger Equation and the Risk Measures’ Theory. We deduce that the Pareto, the Generalized Pareto Distributions and in general the distributions whose support is a pure subset of the positive real numbers, are adequate for the definition of the so-called Quantum Risk Measures. Thanks both to the finite values of them and the relation of these distributions to the Extreme Value Theory, these new Risk Measures may be useful in cases where a discrimination of types of insurance contracts and the volume of contracts has to be known. In the case of use of the Quantum Theory, the mass of the quantum particle represents either the volume of trading in a financial asset, or the number of insurance contracts of a certain type.