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Loss Reserving Using Estimation Methods Designed for Error Reduction

Venter, Gary

Maximum likelihood estimation has been the workhorse of statistics for decades, but alternative methods are proving to give more accurate predictions. The rather vague sounding term “regularization” is used for these. Their basic feature is shrinking fitted values towards the overall mean, much like in credibility. These methods are introduced and applied to loss reserving. Improved estimation of ranges is also addressed, in part by a focus on the variance and skewness of residual distributions. For variance, if large losses pay later, as is typical, the variance in the later columns does not reduce as fast as the mean does. This can be modeled by making the variance proportional to a power of the mean less than 1. Skewness can be modeled using the three-parameter Tweedie distribution, which for a variable Z is reparameterized here in a, b, p to have mean = ab, variance = ab^2, and skewness = p/sqrt(a). Then the distribution of the sum of N individual claims has parameters aN, b, p, and cZ has parameters a, bc, p. These properties are both useful in actuarial applications.

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