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The allocation of losses in life insurance and Hattendorff’s theorem
José Garrido and Tuan Xing |
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This educational note presents proofs of Hattendorff’s theorem for different models,
with increasing level of generality. A deep understanding of the concepts of loss, reserve, and their
relation with accounting conventions and the equivalence principle are key to the loss allocation
in life insurance. We illustrate the fundamental representation of losses as martingales, where
the increment of the martingale gives the allocation of total losses to a one-year (period) term
insurance. This rests on the equivalence principle and the Markov property of the life (multiplestate)
process.
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