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Title: Facing a Risk: To Insure or Not to Insure¿An Analysis with the Constant Relative Risk Aversion Utility Function
Author: Claramunt Bielsa, M. Mercè
Mármol, Maite
Varea, Javier
Keywords: Presa de decisions (Estadística)
Avaluació del risc
Risc (Assegurances)
Statistical decision
Risk assessment
Risk (Insurance)
Issue Date: 21-Feb-2023
Publisher: MDPI
Abstract: The decision to transfer or share an insurable risk is critical for the decision maker’s economy. This paper deals with this decision, starting with the definition of a function that represents the difference between the expected utility of insuring, with or without deductibles, and the expected utility of not insuring. Considering a constant relative risk aversion (CRRA) utility function, we provide a decision pattern for the potential policyholders as a function of their wealth level. The obtained rule applies to any premium principle, any per-claim deductible and any risk distribution. Furthermore, numerical results are presented based on the mean principle, a per-claim absolute deductible and a Poisson-exponential model, and a sensitivity analysis regarding the deductible parameter and the insurer security loading was performed. One of the main conclusions of the paper is that the initial level of wealth is the main variable that determines the decision to insure or not to insure; thus, for high levels of wealth, the decision is always not to insure regardless of the risk aversion of the decision maker. Moreover, the parameters defining the deductible and the premium only have an influence at low levels of wealth.
Note: Reproducció del document publicat a:
It is part of: Mathematics, 2023, vol. 11, num.5
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Appears in Collections:Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

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