Le « risque de montant » des primes de rentes viagères. L'exemple de la loterie-tontine de 1743
It seems that life insurance companies under evaluate an implicit risk occurring whenever contracts with large size differences in life-annuities are present in their portfolio. If, in the case of equal amounts, one might admit that “early” and “late” deaths could compensate one another, this is not really so in the case of, lets say, an early death of a “small” life-annuity and a late “very large” one. In order to put into light this “size effect” on real data one needs first to have at hand a life-insurance portfolio. This was given to us by an original package of the 18th century, the 1743 “tontine-lottery” case, which awarded 5 000 life-annuities (on 30264 tickets). A large simulation of the distribution of winning tickets and of the path of death occurrences shows that this “size risk” does exist. The implication is that the companies should take this risk into account when pricing life-annuities. Classification JEL : G22, N23, C15
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