메뉴 건너뛰기




Volumn 19, Issue 3, 1997, Pages 187-235

Markov models and Thiele's integral equations for the prospective reserve

Author keywords

Actuarial payment function; Backward equations; Markov jump process; Theorem of Cantelli; Thiele's integral equations

Indexed keywords


EID: 0031142822     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(97)00020-6     Document Type: Article
Times cited : (25)

References (36)
  • 6
    • 0010963548 scopus 로고
    • MC Tract, Mathematisch Centrum, Amsterdam
    • Gill, R. (1980). Censoring and stochastic integrals. MC Tract, Vol. 124, Mathematisch Centrum, Amsterdam.
    • (1980) Censoring and Stochastic Integrals , vol.124
    • Gill, R.1
  • 7
    • 0002770442 scopus 로고
    • Lectures on survival analysis
    • D. Bakry, R. Gill and S. Molchanov, eds. Lecture Notes in Mathematics, Springer, Berlin
    • Gill, R. (1994). Lectures on survival analysis. In: D. Bakry, R. Gill and S. Molchanov, eds., Lectures on Probability Theory. Lecture Notes in Mathematics, Vol. 1581, Springer, Berlin.
    • (1994) Lectures on Probability Theory , vol.1581
    • Gill, R.1
  • 8
    • 0001232443 scopus 로고
    • A survey of product-integration with a view toward application in survival analysis
    • Gill, R. and S. Johansen (1990). A survey of product-integration with a view toward application in survival analysis. The Annals of Statistics 18, 1501-1555.
    • (1990) The Annals of Statistics , vol.18 , pp. 1501-1555
    • Gill, R.1    Johansen, S.2
  • 9
    • 0010968517 scopus 로고
    • S. Habermann and T.A. Sibbett, eds.
    • Gram, P. (1910). Professor Thiele as an actuary. In: S. Habermann and T.A. Sibbett, eds., Vol. IV. 237-244.
    • (1910) Professor Thiele as an Actuary , vol.4 , pp. 237-244
    • Gram, P.1
  • 10
    • 0011007638 scopus 로고    scopus 로고
    • Unfinished book manuscript, Mathematisches Institut der Universität zu Köln
    • Helbig, M. and H. Milbrodt (1997). Personenversicherungsmathematik. Unfinished book manuscript, Mathematisches Institut der Universität zu Köln.
    • (1997) Personenversicherungsmathematik
    • Helbig, M.1    Milbrodt, H.2
  • 12
    • 51249188215 scopus 로고
    • Markov chain models in life insurance
    • Hoem, J.M. (1969). Markov chain models in life insurance. Blätter der DGVM IX, 91-107.
    • (1969) Blätter der DGVM , vol.9 , pp. 91-107
    • Hoem, J.M.1
  • 13
    • 0003266062 scopus 로고
    • Inhomogeneous semi-Markov processes, select actuarial tables and duration-dependence in demography
    • T.N.E. Greville, ed. Academic Press, New York
    • Hoem, J.M. (1972). Inhomogeneous semi-Markov processes, select actuarial tables and duration-dependence in demography. In: T.N.E. Greville, ed., Population Dynamics. Academic Press, New York, pp. 251-296.
    • (1972) Population Dynamics , pp. 251-296
    • Hoem, J.M.1
  • 15
    • 0010967619 scopus 로고
    • A characterization of minimal Markov jump processes
    • Jacobsen, M. (1972). A characterization of minimal Markov jump processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 23, 32-46.
    • (1972) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.23 , pp. 32-46
    • Jacobsen, M.1
  • 16
    • 0000531113 scopus 로고
    • Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales
    • Jacod, J. (1975). Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales. Z. Wahrscheinlichkeitstheorie verw. Geb. 31, 235-253.
    • (1975) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.31 , pp. 235-253
    • Jacod, J.1
  • 17
    • 0011003890 scopus 로고
    • Product integrals and Markov processes
    • Johansen, S. (1986). Product integrals and Markov processes. CWI Newsletter 12, 3-13.
    • (1986) CWI Newsletter , vol.12 , pp. 3-13
    • Johansen, S.1
  • 20
    • 84861222798 scopus 로고
    • A stochastic version of Thiele's differential equation
    • Møller, C.M. (1993). A stochastic version of Thiele's differential equation. Scandinavian Actuarial Journal, 1-16.
    • (1993) Scandinavian Actuarial Journal , pp. 1-16
    • Møller, C.M.1
  • 21
    • 0011046369 scopus 로고
    • A counting process approach to stochastic interest
    • Møller, C.M. (1995). A counting process approach to stochastic interest. Insurance: Mathematics and Economics 17, 181-192.
    • (1995) Insurance: Mathematics and Economics , vol.17 , pp. 181-192
    • Møller, C.M.1
  • 22
    • 0011003891 scopus 로고
    • Payment measures, interest and discounting
    • Norberg, R. (1990). Payment measures, interest and discounting. Scandinavian Actuarial Journal, 14-33.
    • (1990) Scandinavian Actuarial Journal , pp. 14-33
    • Norberg, R.1
  • 23
  • 24
    • 0011030917 scopus 로고
    • Hattendorff's theorem and Thiele's differential equation generalized
    • Norberg, R. (1992). Hattendorff's theorem and Thiele's differential equation generalized. Scandinavian Actuarial Journal, 2-14.
    • (1992) Scandinavian Actuarial Journal , pp. 2-14
    • Norberg, R.1
  • 25
    • 0000871435 scopus 로고
    • Differential equations for higher order moments of present values in life insurance
    • Norberg, R. (1995a). Differential equations for higher order moments of present values in life insurance. Insurance: Mathematics and Economics 17, 171-180.
    • (1995) Insurance: Mathematics and Economics , vol.17 , pp. 171-180
    • Norberg, R.1
  • 26
    • 84982465332 scopus 로고
    • A time-continuous Markov chain interest-model with applications to insurance
    • Norberg, R. (1995b). A time-continuous Markov chain interest-model with applications to insurance. Journal of Applied Stochastic Models and Data Analysis 11, 245-256.
    • (1995) Journal of Applied Stochastic Models and Data Analysis , vol.11 , pp. 245-256
    • Norberg, R.1
  • 27
    • 85011455915 scopus 로고    scopus 로고
    • Thiele's differential equation with stochastic interest of diffusion type
    • Norberg, R. and C.M. Moøller (1996). Thiele's differential equation with stochastic interest of diffusion type. Scandinavian Actuarial Journal, 37-49.
    • (1996) Scandinavian Actuarial Journal , pp. 37-49
    • Norberg, R.1    Moøller, C.M.2
  • 28
    • 0010991837 scopus 로고
    • Thiele's differential equation as a tool in product development in life insurance
    • Ramlau-Hansen, H. (1990). Thiele's differential equation as a tool in product development in life insurance. Scandinavian Actuarial Journal, 97-104.
    • (1990) Scandinavian Actuarial Journal , pp. 97-104
    • Ramlau-Hansen, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.