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...

The contribution is devoted to the dependent multiple life insurance of married couple. A more realistic assumption of dependent lifetime of married couple is investigated as distinct from classical approach, which assumes the independent lives. Two models: first is based on the Markov chain and second uses the copulas, mainly Archimedean are studied. The actuarial values of three cases of pensions: widow's, n-year joint-life and n-year last survival annuities are calculated in these models. The differences between the values of pensions in the independent model and model based on the dependences are investigated using the empirical data from Poland. The results will be compare with the results obtained in the author's earlier investigations.

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.

The paper is devoted to the multivariate measures of dependence. In contrast to the classical approach, where the pairs of variables are studied, we investigate the dependence of more than two variables. We mainly consider the measures based on copulas. These are the multivariable generalizations of the known coefficients of such correlation as Spearman's rho, Kendall's tau, Blomquist's beta and Gini's gamma. We present the definitions, the constructions and the basic properties of such multivariate measures of dependence. The case of large number of dimension, greater than two, presents more complications. We have several different versions of such generalization in this case and the lower bound of the values of such measures of dependence are close to zero. We also study the multivariate tail dependences. The last part of the paper is devoted to the estimation of multivariable versions of Spearman's rho coefficient.

In this paper, we investigate non-classical reinsurance models. Two kinds of such models are presented. One is based on dependent binomial distributions and the second on fuzzy numbers. First, we study dependent random variables representing claims using copulas. We investigate the number of claims the reinsurer covers and the total value of covered claims. We present the influence of the degree of dependence and different copulas on the number and the value of the claims covered by the reinsurer. Second, we analyze the case in which the main parameter of the model, the probability that the reinsurer covers the claim, is uncertain. We treat such a parameter as a fuzzy number in this case and combine randomness and fuzziness. We also study the case when the parameter of a copula which describes the degree of dependence is uncertain.