@misc{Heilpern_Stanisław_Marriage_2018,
 author={Heilpern, Stanisław},
 identifier={DOI: 10.15611/sps.2018.16.02},
 year={2018},
 rights={Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy},
 publisher={Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu},
 description={Śląski Przegląd Statystyczny = Silesian Statistical Review, 2018, Nr 16, s. 23-54},
 language={eng},
 abstract={The paper is devoted to marriage insurance contracts allowing dependence between lifetimes of spouses. The dependence structure is described by the five stage Markov process. One state concerns divorce, which was not investigated in previous papers. It makes this paper more realistic. The transition probabilities are derived and the Markov forces of transition are estimated. The four pensions of spouses: the joint-life and last survival annuities, the widow pension and reversionary annuity are introduced and studied. A real example based on the data from Lower Silesia during 2011 is investigated. The values of these annuities are computed and analyzed. The five different cases are studied. The impact of the age of spouses and the duration of annuities on the values of annuities is investigated. A case when the reversionary annuity with the reduction parameter R = 2/3 is analyzed. A comparison with a non-divorce case is considered},
 title={Marriage insurance taking into account dependence and divorces},
 type={artykuł},
 keywords={marriage insurance, dependence, Markov chain, annuities, divorce, ubezpieczenia małżeńskie, zależność, łańcuch Markowa, renty, rozwody},
}