Statistical Aspects of Perpetuities

Rudolf Grübel and Susan M. Pitts

Journal of Multivariate Analysis, 2000, vol. 75, issue 1, 143-162

Abstract: For a distribution [mu] on the unit interval we define the associated perpetuity [Psi]([mu]) as the distribution of 1+X1+X1X2+X1X2X3+..., where (Xn)n[set membership, variant] is a sequence of independent random variables with distribution [mu]. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functional[psi] with respect to integral and supremum norms. These results are then used to investigate the statistical properties of empirical perpetuities, including the behaviour of bootstrap confidence regions.

Keywords: perpetual annuity; empirical perpetuities; asymptotic normality; bootstrap (search for similar items in EconPapers)
Date: 2000
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