Economics - Research Publications

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APRA general insurance risk margins

Taylor, Greg ( 2006-02)

It is common for actuaries to estimate percentile-based risk margins on the assumption of a log normal distribution of liability, together with an estimate of coefficient of variation ("CoV"). This can yield seemingly anomalous results, with percentage risk margin decreasing as CoV increases. The mathematics of this type of risk margin is explored. An APRA risk margin is the maximum of this type and a multiple of CoV. Such risk margins are studied in a more general setting than APRA's, with both percentile p and CoV multiple k free. The APRA risk margins form a special case within this setting.Particular attention is paid to risk margin transition points, values of the log normal dispersion parameter at which the risk margin changes from one form to the other as that parameter increases. For given values of p and k, the existence, uniqueness and location of transition points is investigated. The direction of change of a transition point in the presence of increasing p or k is alsoinvestigated. Various numerical examples are given.