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Grzegorz Rogoziński
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Beata DębskaArticles published in the form submitted by the authors All rights reserved. No part of this book may be reproduced in any form or in any means without the prior permission in writing of the Publisher
The purpose of the paper is applying the generalized model of reversionary annuity to determine the benefit of marriage reverse annuity contracts and reverse mortgages. First of all, benefits depend on the age of spouses, their future lifetime and the real value of their properties which, in turn, determines the place where they live. In addition, the frequency of payments affects the amount of benefit. Therefore, the periodic benefits are determined for some regions of Poland on the basis of real Polish data from 2015, which mostly comes from The Central Statistical Office of Poland. Calculations of annuities are based on the fixed interest rate and the interest rate function depending on time t for Polish real data. The results are later compared.
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 future lifetimes between spouses are dependent. The structure of dependence of the length of spouses' lives is modelled using copulas. The term structure of interest rate is modelled using a time-dependent function. The numerical results are based on actual Polish data covering both the structure of the probabilistic model and the interest rate.
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