Pricing Marriage Insurance with Mortality Dependence

• Autorzy: Joanna Dębicka , Stanisław Heilpern , Agnieszka Marciniuk
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Insurance contract; Marriage; Life insurance; Life expectancy

PL

Umowa ubezpieczeniowa; Małżeństwo; Ubezpieczenia na życie; Długość życia

• Czasopismo: Central European Journal of Economic Modelling and Econometrics (CEJEME)
• Rocznik: 2023
• Tom: 15
• Numer: nr 1
• Strony: 31--64

Twórcy

autor

Joanna Dębicka

• Wrocław University of Economics and Business, Wrocław, Poland

autor

Stanisław Heilpern

• Wrocław University of Economics and Business, Wrocław, Poland

autor

Agnieszka Marciniuk

• Wroclaw University of Economics and Business, Poland

Bibliografia

• [1] Carriere J. F., (2000), Bivariate Survival Models for Coupled Lives, Scandinavian Actuarial Journal 1, 17-31.
• [2] Denuit M., Dhaene J., Le Bailly de Tillegheim C., Teghem S., (2001), Measuring the impact of a dependence among insured lifelengths, Belgian Actuarial Bulletin 1(1), 18-39.
• [3] Dębicka J. (2003), Moments of the cash value of future payment streams arising from life insurance contracts, Insurance: Mathematics and Economics 33, 533550.
• [4] Dębicka J. (2013), An approach to the study of multistate insurance contracts, Applied Stochastic Models in Business and Industry 29(3), 224-240.
• [5] Dębicka J., Heilpern S., Marciniuk A., (2016), Profitability of marriage insurance contract, [in:] 19-th AMSE. Applications of Mathematics in Economics (Conference Proceedings). International Scientific Conference: Banska Stiavnica, Slovakia, 31 Aug.-4 Sep. 2016.
• [6] Dębicka J., Heilpern S., and Marciniuk A., (2022), Modelling Marital Reverse Annuity Contract in a Stochastic Economic Environment, Statistika 102(3), 261281.
• [7] Durrleman V., Nikeghbali, A., Roncalli, T., (2000), Which copula is right now?, Groupe de Recherche Operationnelle, Credit Lyonnais, Working Papers.
• [8] Embrechts P., Lindskog F., McNeil A. J., (2003), Modeling Dependence with Copulas and Applications to Risk Management, [in:] S. Rachev (ed.), Handbook of Heavy Tailed Distributions in Finance, 329-384, Elsevier, Rotterdam.
• [9] European Central Bank, (2020), access 17-07-2020, available at: htps://www.ecb.europa.eu/stats/financial_markets_and_interest_ rates/euro_area_yield_curves/html/index.en.html.
• [10] Eurostat, (2020), access 16-03-2020, available at: https://ec.europa.eu/ eurostat/data/database.
• [11] Frees E. W., (1990), Stochastic life contingencies with solvency considerations, Transactions of the Society of Actuaries XLII, 91-148.
• [12] Genest C., Mackay J., (1986), The joy of copula: bivariate distributions with uniform margins, The American Statistician 40, 280-283.
• [13] Genest C., Rivest L. P., (1993), Statistical inference procedures for bivariate Archimedean copulas, Journal of the American Statistical Association 88, 10341043.
• [14] Gourieroux C., Lu Y., (2015), Love and death: A Freund model with frailty, Insurance: Mathematics and Economics 63, 191-203.
• [15] Haberman S., Pitacco E., (1999), Actuarial Models for Disability Insurance, Chapman & Hall CRC, Londyn.
• [16] Heilpern S., (2007), Funkcje łączące. Wydawnictwo Akademii Ekonomicznej we Wrocławiu, Wrocław.
• [17] Heilpern S., (2015), Dependent structure induced by Markov chain in the multiple life insurance, [in:] 18-th International Scientific Conference Applications of Mathematics in Economics, Jindrichuv Hradec.
• [18] Henshaw K., Constantinescu C., Menoukeu Pamen O., (2020), Stochastic Mortality Modelling for Dependent Coupled Lives, Risks 8, 17.
• [19] Hoem J. M., (1969), Markov Chain Models in Life Insurance, Blätter der Deutschen Gesellschaft für Versicherungsmathematik IX, 91-107.
• [20] Hoem J. M., (1988), The Versality of the Markov Chain as a Tool in the Mathematics of Life Insurance, Transactions of the 23rd International Congress of Actuar^les, Helsinki, Vol. R, 171-202.
• [21] Ji M., Hardy M., Siu-Hang Li J., (2011), Markovian Approaches to Joint-Life Mortality, North American Actuarial Journal 15(3), 357-376.
• [22] Luciano E., Spreeuw J., Vigna E., (2008), Modeling stochastic mortality for dependent lives, Insurance: Mathematics and Economics 43, 234-244.
• [23] Luciano E., Spreeuw J., Vigna E., (2016), Spouses' Dependence across Generations and Pricing Impact on Reversionary Annuities, Risks 4(2), 1-18.
• [24] Marciniuk A., (2009), Nielosowe modele natychmiastowej stopy procentowej i ich zastosowanie w klasycznych ubezpieczeniach życiowych, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu. Ekonometria 27, 112-127.
• [25] Nelsen R. B., (1999), An Introduction to Copulas, Springer, New York.
• [26] Norberg R., (1989), Actuarial analysis of dependent lives. Bulletin de l'Association Suisse des Actuaries 40, 243-254.
• [27] Parker G., (1994), Stochastic Analysis of Portfolio of Endowment Insurance Policies, Scandinavian Actuarial Journal 77(2), 119-130.
• [28] Spreeuw J., (2006), Types of dependence and time-dependent association between two times in single parameter copula models, Scandinavian Actuarial Journal 5, 286-309.
• [29] The Czech Statistical Office Life Tables, access: 16-03-2020, available at: https://www.czso.cz/csu/czso/life-tables-for-the-czech-republic-cohesion-regions-and-regions-2016-2017.
• [30] Wolthuis H., (1994), Life insurance mathematics (The Markovian model), CAIRE education Series, No. 2, Bruxelles.
• [31] Wolthuis H., Van Hoek I., (1986), Stochastic models for life contingencies, Insurance: Mathematics and Economics 5, 217-254.

Identyfikatory

DOI

10.24425/cejeme.2023.144998