In this paper, we present a threshold proportional reinsurance strategy and we analyze the effect on some solvency measures: ruin probability and time of ruin. This dynamic reinsurance strategy assumes a retention level that is not constant and depends on the level of the surplus. In a model with inter-occurrence times being generalized Erlang(n)-distributed, we obtain the integro-differential equation for the Gerber–Shiu function. Then, we present the solution for inter-occurrence times exponentially distributed and claim amount phase-type(N). Some examples for exponential and phase-type(2) claim amount are presented. Finally, we show some comparisons between threshold reinsurance and proportional reinsurance.

Most insurance policies include a deductible, so that a part of the claim is paid by the insured. In order to get full coverage of the claim, the insured has two options: purchase a Zero Deductible Insurance Policy or purchase an insurance policy with deductible together with Refundable Deductible Insurance. The objective of this paper is to analyze these two options and compare the premium paid by each. We define dif(P) 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 allow us to obtain the greatest reduction in the premium.

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.

This paper investigates the potential of reverse mortgages (RMs) to alleviate poverty among older adults living alone in Spain, focusing on both general effects and gender-specific disparities. Using a combined income-wealth approach, the analysis highlights the role of housing equity, which is often the primary asset for older homeowners. While previous research has examined the impact of RMs on poverty rates among the broader population aged 65 and over, this work narrows its scope to single-person households, a growing and particularly vulnerable subgroup facing significant economic and social challenges. The findings reveal that RMs can reduce poverty rates, improve the financial well-being of these households and decrease gender disparities. Thus, the work shows RMs as a policy tool to improve the economic situation and quality of life for older adults living alone and underscores the need for targeted strategies to address gender-specific vulnerabilities.

In this paper we apply the modal interval theory to the actuarial field to study the analysis and control of solvency in non-life insurance portfolios. The advantages of modal intervals over classical intervals are the interpretative field and the extension of the calculation possibilities that modal intervals offer. To achieve this, we will analyse and propose some properties of modal interval probability that allow us to ensure that the cumulative distribution function and the probability density function of the aggregated cost with which we will work are modal interval functions and, therefore, they can be correctly interpreted from this new point of view.