Refundable deductible insurance

Most insurance policies include a deductible, so that a part of the claim is assumed by the insured. In order to get a full coverage of the claim, the insured has two options: hire a Zero Deductible Insurance or take out an insurance policy with deductible and, simultaneously, a Refundable Deductible Insurance. The objective of this paper is to analyze these two options, comparing the premium paid. We define dif (F) as the difference between the premiums paid. This function depends on the parameters of the deductible applied, and we focus our attention on the sign of this difference and the calculation of the optimal deductible, that is, the values of the parameters of the deductible that allows us to obtain the greatest reduction in the global premium.