Abstract
In this paper, we define a retrospective accumulated net asset random variable and mathematically demonstrate that its expectation is the retrospective reserve which in turn is equivalent to the prospective reserve. We further explore various properties of this retrospective accumulated net asset random variable. In particular, we find and demonstrate that this retrospective random variable can be used as a tool for helping us extract historical information on the pattern and significance of deviation of actual experience from that assumed for reserving purposes. This information can subsequently guide us as to whether it becomes necessary to adjust prospective reserves and the procedure to do so. The paper concludes, as an illustration, with a model of a block of in force policies with actual experience different from reserving assumptions and a suggested methodology on how prospective reserves could be adjusted based on the realized retrospective accumulated net asset random variable.
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Acknowledgements
The Goldenson Center wishes to acknowledge Pratish Modi, a graduate student in actuarial science at the University of Connecticut and Ruth Nieh, a junior Honors student also at the University of Connecticut who did her honors thesis on this topic, for their assistance in this research project. The authors also appreciate the comments and suggestions made by the reviewer which helped improve the final version of this paper.
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Vadiveloo, J., Niu, G., Valdez, E.A., Gan, G. (2017). Unlocking Reserve Assumptions Using Retrospective Analysis. In: Londoño, J., Garrido, J., Jeanblanc, M. (eds) Actuarial Sciences and Quantitative Finance. ICASQF 2016. Springer Proceedings in Mathematics & Statistics, vol 214. Springer, Cham. https://doi.org/10.1007/978-3-319-66536-8_2
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DOI: https://doi.org/10.1007/978-3-319-66536-8_2
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