Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function

M. Mercè Claramunt, Maite Mármol () and Xavier Varea
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M. Mercè Claramunt: Department of Mathematics for Economics, Finance and Actuarial Science, Faculty of Economics and Business, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain
Maite Mármol: Department of Mathematics for Economics, Finance and Actuarial Science, Faculty of Economics and Business, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain
Xavier Varea: Department of Mathematics for Economics, Finance and Actuarial Science, Faculty of Economics and Business, University of Barcelona, Avinguda Diagonal 690, 08034 Barcelona, Spain

Mathematics, 2023, vol. 11, issue 5, 1-13

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.

Keywords: decision analysis; risk analysis; CRRA utility function; deductible (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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