Abstract
A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves of an insurance company. The following methodology relies on the Dirac matrix formalism and the Feynman path-integral method.
Highlights
The theory of non-life insurance risk is a major topic in actuarial sciences
This paper proposes a quantum-type approach for the representation and analysis of non-life insurance data
Quantum mechanics methods are successfully applied in various disciplines, including finance for option pricing (e.g., Baaquie 2007, 2010) and econophysics for risk management (e.g., Bouchaud and Potters 2003; Mantegna and Stanley 2000)
Summary
This paper proposes a quantum-type approach for the representation and analysis of non-life insurance data. Quantum mechanics methods are successfully applied in various disciplines, including finance for option pricing (e.g., Baaquie 2007, 2010) and econophysics for risk management (e.g., Bouchaud and Potters 2003; Mantegna and Stanley 2000). Their application to insurance, is an emerging field of research that has been introduced recently in Tamturk and Utev (2018). The current approach is new and consists in representing the observations on an insurance risk in the form of quantum data, that is to say from a quantum mechanical type model
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