23.2 Impact of Parameter Risk

CoV for total losses if the frequency and severity distribution are known

\[\begin{equation} CV^2(S) = \underbrace{CV^2(N)}_{\text{# of Claims}} + \underbrace{\dfrac{CV^2(X)}{\mu_N}}_{\text{Severity}} \tag{23.1} \end{equation}\]

• For large company, \(\mu_N\) is large so the 2^nd term is small

• \(S\) = Total losses

• \(X\) = Severity

• \(N\) = Numbers of claims

However if we add systemic factor that impacts all claims (e.g. inflation), it doesn’t diversify away as the # of expected claims \(\uparrow\)

• Relative impact on large company is much bigger since their process variance is small

For small company there is a large amount of process risk so the overall variability does not increase very much