PL EN


2012 | 10(16) | 39-55
Article title

Matrix approach to analysis of a portfolio of multistate insurance contracts

Authors
Title variants
Languages of publication
EN
Abstracts
EN
This paper discusses the calculation of moments of cash value of future payment streams arising from portfolio of multistate insurance contracts, where the evolution of the insured risk and the interest rate are random. A matrix form for formulas for the first two moments of cash value of the stream of future payments for a portfolio of policies is derived. As an application formulas for insurance premiums are provided. The general theory is illustrated with a case where the rate of interest is modeled by a Wiener and an Ornstein-Uhlenbeck process.
Contributors
References
  • Dębicka J., Moments of the cash value of future payment streams arising from life insurance contracts, “Insurance: Mathematics and Economics” 2003, 33, pp. 533-550.
  • Dębicka J., Macierzowa reprezentacja ubezpieczenia wielostanowego z niejednorodnym lańcuchem Markowa, [w:] Statystyka aktuarialna − stan i perspektywy rozwoju w Polsce, red. W. Ostasiewicz, Prace Naukowe Akademii Ekonomicznej we Wrocławiu 1108, Wydawnictwo Akademii Ekonomicznej, Wrocław 2006, pp. 244-265.
  • Dębicka J., An approach to the study of multistate insurance contracts, “Applied Stochastic Models in Business and Industry” 2012, Bus. 2012, Ind.. doi: 10.1002/asmb.1912.
  • Frees E.W., Stochastic life contingencies with solvency considerations, “Transactions of the Society of Actuaries” 1990, XLII, pp. 91-148.
  • Gregorius F.K., Disability insurance in The Netherlands, “Insurance: Mathematics and Economics” 1993, 13, pp. 101-116.
  • Hoem J.M., Markov chain models in life insurance, “Blätter der Deutschen Gesellschaft für Versicherungsmathematik” 1969, vol. IX, pp. 91-107.
  • Hoem J.M., The Versality of the Markov Chain as a Tool in the Mathematics of Life Insurance, “Transactions of the 23rd International Congress of Actuaries” 1988, vol. R, pp. 171-202.
  • Parker, G. (1994). Stochastic Analysis of Portfolio of Endowment Insurance Policies.
  • Scandinavian Actuarial Journal, 77 (2), pp. 119-130.
  • Rocznik Demograficzny 2010, Zakład Wydawnictw Statystycznych, GUS, Warszawa 2010.
  • Waters H.R., An approach to the study of multiple state models, “Journal Institute of Actuaries” 1984, vol. 111, part II, no 448, pp. 363-374.
  • Wolthuis H., Life insurance mathematics (The Markovian model), CAIRE Education Series, no 2, Bruxelles 1994.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-2a8d5cb2-933a-40c4-bf95-cdbb43324b7e
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.