Asmussen, S. (2000). Ruin probabilities, volume 2 of Advance series on statistical science &
applied probability. World Scientific, River Edge, N.J.
Assaf, D., Langberg, N. A., Savits, T. H., and Shaked, M. (1984). Multivariate phase-type
distributions. Operations Research, pages 688–702.
Cai, J. and Li, H. (2005a). Conditional tail expectations for multivariate phase-type
distributions. Journal of Applied Probability, pages 810–825.
Cai, J. and Li, H. (2005b). Multivariate risk model of phase type. Insurance: Mathematics
and Economics, pages 137–152.
Carriere, J. F. (2000). Bivariate survival models for coupled lives. Scandinavian Actuarial
Journal, pages 17–32.
Dickson, D. C. M., Hardy, M., and Waters, H. R. (2013). Actuarial Mathematics for Life
Contingent Risks. Cambridge.
Drekic, S., Dickson, D. C., Stanford, D. A., andWillmot, G. E. (2004). On the distribution
of the deficit at ruin when claims are phase-type. Scandinavian Actuarial Journal, pages
105–120.
Frees, E. W., Carriere, J., and Valdez, E. (1996). Annuity valuation with dependent
mortality. Journal of Risk and Insurance, pages 229–261.
Hassan Zadeh, A. (2009). Actuarial applications of multivariate phase-type distributions:
Model calibration and credibility. PhD thesis, Universite des Montreal.
Hassan Zadeh, A. and Bilodeau, M. (2013). Fitting bivariate distributions with phasetype
distributions. Scandinavian Actuarial Journal, 2013:241–262.
Hassan Zadeh, A., Jones, B. L., and Stanford, D. A. (2014). The use of phase-type models
for disability insurance calculations. Scandinavian Actuarial Journal, pages 714–728.
Hassan Zadeh, A. and Stanford, D. A. (2016). Bayesian and bühlmann credibility for
phase-type distributions with a univariate risk parameter. Scandinavian Actuarial
Journal, pages 338–355.
Henshaw, K., H. W. C. C. and Khalil, D. (2023). Dependence modelling of lifetimes in
egyptian families. Risks, 11:1–18.
Spreeuw, J., and Owadally, I. (2013). Investigating the broken-heart effect: a model
for short-term dependence between the remaining lifetimes of joint lives. Annals of
Actuarial Science, pages 236–257.
Ji, M. (2011). Markovian Approaches to Joint-life Mortality with Applications in Risk Management.
PhD thesis, University of Waterloo.
Ji, M., Hardy, M., and Li, J. S. H. (2011). Markovian approaches to joint-life mortality.
North American Actuarial Journal, pages 357–376.
Lin, X. S. and Liu, X. (2007). Markov aging process and phase-type law of mortality.
North American Actuarial Journal, pages 92–109.
Luciano, E., Spreeuw, J., and Vigna, E. (2008). Modelling stochastic mortality for
dependent lives. Insurance: Mathematics and Economics, pages 234–244.
Neuts, M. (1981). Matrix-geometric solutions in stochastic models, volume 2 of John Hoplins
Series in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, Md.
Parkes, M. C. and Brown, R. J. (1972). Health after bereavement: A controlled study of
young boston widows and widowers. Psychosomatic Medicine, page 449461.
Sverdrup, E. (1965). Estimates and test procedures in connection with stochastic models
for deaths, recoveries and transfers between different states of health. Scandinavian
Actuarial Journal, pages 184–211.
The MathWorks, I. (2023). Matlab r2023b. Accessed: 2023-03-15.
Young, M., Benjamin, B., and Wallis, C. (1963). The mortality of widowers. Lancet,
pages 454–6.
Zang, Y. (2013). Credibility with Phase–type Distributions. PhD thesis, University of
Western Ontario.
Zhang, Y. and Brockett, P. (2020). Modeling stochastic mortality for joint lives through
subordinators. Insurance: Mathematics and Economics, 95.
Journal of the Iranian Statistical Society