Journal of Mathematical Finance, 2016, 6, 43-47 Published Online February 2016 in SciRes. http://www.scirp.org/journal/jmf http://dx.doi.org/10.4236/jmf.2016.61005 How to cite this paper: Kountzakis, C.E. and Koutsouraki, M.P. (2016) On Quantum Risk Modelling. Journal of Mathematical Finance, 6, 43-47. http://dx.doi.org/10.4236/jmf.2016.61005 On Quantum Risk Modelling Christos E. Kountzakis, Maria P. Koutsouraki Department of Mathematics, University of the Aegean, Karlovassi, Samos, Greece Received 12 May 2015; accepted 14 February 2016; published 17 February 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract This paper is devoted to the connection between the probability distributions which produce so- lutions of the one-dimensional, time-independent Schrödinger Equation and the Risk Measures’ Theory. We deduce that the Pareto, the Generalized Pareto Distributions and in general the dis- tributions whose support is a pure subset of the positive real numbers, are adequate for the defi- nition 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 use- ful 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 repre- sents either the volume of trading in a financial asset, or the number of insurance contracts of a certain type. Keywords Hamiltonian, Eingenvalues, Continuous Spectrum, Quantum Risk Measure 1. Introduction As it is mentioned in [1], the cause for the use of the use of quantum theory in risk models and finance is their complexity, in the sense that the return of an asset or the value of it depends on several factors. At this point we may quote that though there exists a broad literature in finance which relies on the notions of quantum mechanics, there is a lack of literature which connects quantum mechanics’ modelling and risk theory. A semi- nal reference in quantum finacnce is the paper under the same title [2], which refers to the basics of this subject. Another essential reference is [3], which is more related to asset pricing. The other book [4] by the same author is related to interest rates and bond pricing. We write this paper in order to contribute in the research on the relation between quantum finance and risk theory where there is not so much literature. A central role in the theory of risk models recently belongs to the risk measures. Since the main objective of this paper is the risk measures on Hamiltonian operators, it is useful to remind some essential notions from quantum theory, which are useful in the sequel (see [5]).