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2018 | 10 | nr 1 | 27--52
Tytuł artykułu

A Multiple State Model for Premium Calculation when Several Premium-Paid States are Involved

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The aim of this contribution is to derive a general matrix formula for the net period premium paid in more than one state. In order to avoid "overpayment" which implies higher premiums we give a formula for replacement of lump sum benefit into annuity benefits paid in more than one state. The obtained result is useful for example to more advanced models of dread disease insurances allowing period premiums paid by both healthy and ill person (e.g. not terminally yet). As an application, we supply analysis of dread disease insurances against the risk of lung cancer based on the actual data for the Lower Silesian Voivodship in Poland. (original abstract)
Opis fizyczny
  • Wrocław University of Economics, Poland
  • Wrocław University of Economics, Poland
  • [1] Brink A. (2010), Practical example of split benefit accelerated critical illness insurance product. Transitions of the 29th International Congress of Actuaries, Cape Town, South Africa, pp. 677-703.
  • [2] Dash A. Grimshaw D. (1993), Dread Diseasecover - an actuarial perspective. Journal of the Staple Inn Actuarial Society 33, 149-193.
  • [3] Dębicka J., Heilpern S. (2017), Investors expected profit fram viatical settlements. [In:] Proceedings of 20-th AMSE. Applications of Mathematics in Economics. International Scientific Conference, Szklarska Poręba, Poland, pp. 105-116.
  • [4] Dębicka J., Heilpern S., Marciniuk A. (2016), Profitability of marriage insurance contracts. [In:] Proceedings of 19-th AMSE. Applications of Mathematics in Economics. International Scientific Conference, Banská Štiavnica, Slovakia, pp. 66-78.
  • [5] Dębicka J., Zmyślona B. (2015), Modelling of lung cancer survival data for critical illness insurances. available at arXiv:1602.08696.
  • [6] Dębicka J., Zmyślona B. (2016), Construction of multi-state life tables for critical illness insurance - influence of age and sex on the incidence of health inequalities. Silesian Statistical Review 14, 41-63.
  • [7] Dębicka J. (2003), Moments of the cash value of future payment streams arising from life insurance contracts. Insurance: Mathematics and Economics 33 (3), 533-550.
  • [8] Dębicka J. (2010), Macierzowa reprezentacja rezerw w ubezpieczeniach wielostanowych. Rocznik Kolegium Analiz Ekonomicznych 33 (21), 73-96.
  • [9] Dębicka J. (2013), An approach to the study of multistate insurance contracts. Applied Stochastic Models in Business and Industry 29(3), 224-240.
  • [10] Dijkstra E. (1959), A note on two problems in connexion with graphs. Numer. Math. 1(1), 269-271.
  • [11] Frees E. (1990), Stochastic life contingencies with solvency considerations. [In:] Proceedings di 2nd Conference in Actuarial Science and Finance on Samos, Karlovassi (Grecia), proceedSibillo.pdf, pp. 91-129.
  • [12] Gala K. (2013), Analiza ubezpieczeń dla wielu osób z wykorzystaniem funkcji copula. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocawiu (312), 50-56.
  • [13] Haberman S., Pitacco E. (2012), Actuarial Models for Disability Insurance. Chapman & Hall/CRC.
  • [14] Hoem J. (1969), Markov chain models in life insurance. Blätter der DGVFM 9(2), 91-107.
  • [15] Hoem J. (1988), The versaltility of the markov chain as a tool in the mathematics of life insurance. [In:] Transactions of the 23rd International Congress of Actuaries, Helsinki, Volume R, pp. 171-202.
  • [16] Life Tables of Poland (2008), Available at population/life-expectancy/.
  • [17] NHF (2014), Data base of histories of hospitalization from Lower Silesia Department of National Health Fund. Unpublished due to confidentiality.
  • [18] Parker G. (1994), Stochastic analysis of a portfolio of endowment insurance policies. Scandinavian Actuarial Journal 1994(2), 119-130.
  • [19] Pitacco E. (2014), Health Insurance. Basic Actuarial Models. EAA Series, Springer.
  • [20] Pittaco E. (1994), LTC insurance. From the multistate model to practical implementations. [In:] Proceedings of the XXV ASTIN Colloquium, Cannes, France, pp. 437-452.
  • [21] Waters H.R.(1984), An approach to the study of multiple state models.Journal of the Institute of Actuaries 111(2), 363-374.
  • [22] Wojciechowska U., Didkowska J. (2014), Zachorowania i zgony na nowotwory złośliwe w Polsce. Krajowy Rejestr Nowotworów, Centrum Onkologii - Instytut im. Marii Skłodowskiej-Curie. Available at: (date 10.04.2014).
  • [23] Wolthuis H. (1994), Life insurance mathematics (The Markovian model). Brussels, Belgium : CAIRE.
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