Aggregate Markov models in life insurance: estimation via the EM algorithm

References

• Aalen, O. O., Borgan, Ø. & Gjessing, H. K. (2008). Survival and event history analysis: a process point of view. Statistics for Biology and Health. New York, NY: Springer New York.
   Google Scholar
• Ahmad, J., Bladt, M. & Bladt, M. (2023a). Estimating absorption time distributions of general Markov jump processes. Scandinavian Journal of Statistics, 1–30. doi:10.1111/sjos.12679
   Web of Science ®Google Scholar
• Ahmad, J., Bladt, M. & Furrer, C. (2023b). Aggregate Markov models in life insurance: Properties and valuation. Insurance: Mathematics and Economics 113, 50–69.
   Web of Science ®Google Scholar
• Albrecher, H. & Bladt, M. (2019). Inhomogeneous phase-type distributions and heavy tails. Journal of Applied Probability 56(4), 1044–1064.
   Web of Science ®Google Scholar
• Albrecher, H., Bladt, M. & Müller, A. (2023). Joint lifetime modeling with matrix distributions. Dependence Modeling 11(1), 1–22.
   Web of Science ®Google Scholar
• Albrecher, H., Bladt, M. & Yslas, J. (2022). Fitting inhomogeneous phase-type distributions to data: the univariate and the multivariate case. Scandinavian Journal of Statistics 49(1), 44–77.
   Web of Science ®Google Scholar
• Andersen, P. K. (1993). Statistical models based on counting processes. Springer Series in Statistics, 1st ed. New York, NY: Springer New York.
   Google Scholar
• Asmussen, S., Nerman, O. & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics 23(4), 419–441.
   Web of Science ®Google Scholar
• Bladt, M., Gonzalez, A. & Lauritzen, S. L. (2003). The estimation of phase-type related functionals using Markov chain Monte Carlo methods. Scandinavian Actuarial Journal 2003(4), 280–300.
   Google Scholar
• Bladt, M. & Yslas, J. (2023). Phase-type mixture-of-experts regression for loss severities. Scandinavian Actuarial Journal 2023(4), 303–329.
   Web of Science ®Google Scholar
• Breuer, L. (2002). An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure. Annals of Operations Research 112(1), 123–138.
   Web of Science ®Google Scholar
• Breuer, L. (2003). From Markov jump processes to spatial queues. Dordrecht: Springer Science & Business Media.
   Google Scholar
• Buchardt, K., Møller, T. & Schmidt, K. B. (2015). Cash flows and policyholder behaviour in the semi-Markov life insurance setup. Scandinavian Actuarial Journal 2015(8), 660–688.
   Web of Science ®Google Scholar
• Christiansen, M. C. (2012). Multistate models in health insurance. Advances in Statistical Analysis 96(2), 155–186.
   Web of Science ®Google Scholar
• Gill, R. D. & Johansen, S. (1990). A survey of product-integration with a view toward application in survival analysis. Annals of Statistics 18(4), 1501–1555.
   Web of Science ®Google Scholar
• Helwich, M. (2008). Durational effects and non-smooth semi-Markov models in life insurance. PhD thesis, University of Rostock.
   Google Scholar
• Hoem, J. M. (1969). Purged and partial Markov chains. Scandinavian Actuarial Journal 1969(3-4), 147–155.
   Google Scholar
• Hoem, J. M. (1972). Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography. In T. N. E. Greville, editor, Population Dynamics. New York: Academic Press. P. 251–296.
   Google Scholar
• Johansen, S.. (1986). Product integrals and Markov processes. CWI Newsletter 12, 3–13.
   Google Scholar
• Latouche, G. & Ramaswami, V. (1999). Introduction to matrix analytic methods in stochastic modeling, ASA-SIAM Series on Statistics and Applied Mathematics. SIAM.
   Google Scholar
• Neuts, M. F. (1978). Renewal processes of phase type. Naval Research Logistics Quarterly 25(3), 445–454.
   Google Scholar
• Norberg, R. (1991). Reserves in life and pension insurance. Scandinavian Actuarial Journal 1991, 3–24.
   Google Scholar
• Rydén, T. (1994). Parameter estimation for Markov modulated Poisson processes. Communications in Statistics: Stochastic Models 10(4), 795–829.
   Google Scholar