We model the probabilistic structure and cash flows arising from marriage reverse annuity contracts in the case of the joint-life status and the last surviving status. In contrast to the classical approach, we take into consideration that futu...

Modelling of critical illness survival data, being primary developed in the context of, e.g. health insurance contracts, also plays an important role in the currently analysed problems related to secondary insurance market. The aim of this contribution is two-fold. In the first part we describe how to construct a multiple state model for critical illness insurances, which takes into account that a probability of death for a dread disease sufferer depends on the duration of the disease and the survival probabilities are related to the disease stage. Then, in the second part, we focus on modelling of the probabilistic structure of the analysed model for a particular case of dread disease. Based on the actual data for the Lower Silesian Voivodship in Poland, we estimate the transition probabilities for the derived model in case of the risk of lung cancer. For this purpose we use the methodology developed for the construction of multi-state life tables, such as binomial, Poisson and ordinal logistic regression models. The obtained results can be directly used to build the multiple increment–decrement tables, which are useful to valuation not only critical illness insurances and life insurances with accelerated death benefits option but also to viatical settlement contracts and health-related expenses.

Accurate determination of the probability structure of the multistate model is significant from the valuation and profitability assessment of insurance contracts standpoint. This article aims to analyse the effect of spouses' future lifetime dependence on premiums and prospective reserves for marriage insurance contracts. As a result, under the assumptions that the evolution of the insured risk is described by a nonhomogeneous Markov chain and the dependence between spouses' future lifetime is modelled by the copula, we derive formulas for the elements of the transition matrices. Based on actual data, we conduct a comparative analysis of actuarial values for three scenarios related to future lifetimes of husband and wife. We test the robustness of premium value to the changing degree of dependency between spouses' future lifetimes.

Population ageing is reshaping European economies, including Poland, and calls for analytical approaches capable of identifying structural changes in income composition among older individuals. The aim of this article is to demonstrate the applicability of a method for detecting distinctive structural changes in income sources, using seniors aged 50 and over in Poland as an empirical example. The analysis is based on EU-SILC microdata for the years 2016, 2020, and 2024, combining a structural similarity test with an approach that identifies distinctive relative changes in income composition. The application of the method shows that it captures income structure changes associated with both institutional and economic shocks, in particular the statutory retirement-age reform, implemented in 2017 and the COVID-19 pandemic. Among women aged 60–64, an increasing combination of pension income and earnings from work is observed, while men aged 65–69 display rising labour income despite formal retirement eligibility. During the pandemic period, the method reveals shifts in the relative importance of self-employment and selected social benefits, especially among older age groups and women, which are only partially reflected in standard similarity test results. From a practical perspective, the proposed approach may be useful for analysing income structures of ageing populations and for identifying subtle but economically meaningful changes relevant to pension policy and labour market measures. By illustrating the method using the case of seniors’ incomes in Poland, the study contributes to methodological discussions on the analysis of structural change in socio-economic research.