excans:059393ed48: Difference between revisions
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(Created page with "'''Key: C''' <math display = "block"> \operatorname{E}[ X \wedge 500 ) = \exp(4.2 + \frac{1.1^2}{2}) \Phi(0.73) + 500(1-\Phi(1.83)) = 110.5 </math> Let S denote the aggreg...") |
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<math display = "block"> | <math display = "block"> | ||
\operatorname{E}[ X \wedge 500 | \operatorname{E}[ X \wedge 500 ] = \exp(4.2 + \frac{1.1^2}{2}) \Phi(0.73) + 500(1-\Phi(1.83)) = 110.5 | ||
</math> | </math> | ||
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<math display = "block"> | <math display = "block"> | ||
\begin{aligned} | \begin{aligned} | ||
&\operatorname{E}[ S | &\operatorname{E}[ S ] = \operatorname{E}[ N ] \operatorname{E}[ X \wedge 500] = 20(110.5) = 2210 \\ | ||
&\operatorname{E}[ S | &\operatorname{E}[ S ] = \operatorname{E}[ N ]\operatorname{E}[ X \wedge 500] + \operatorname{E}[ ( X \wedge 500)^ 2 )\operatorname{E}[ N ] = 20(26,189) = 523, 780 | ||
\end{aligned} | \end{aligned} | ||
</math> | </math> | ||
Latest revision as of 13:47, 14 May 2023
Key: C
[[math]]
\operatorname{E}[ X \wedge 500 ] = \exp(4.2 + \frac{1.1^2}{2}) \Phi(0.73) + 500(1-\Phi(1.83)) = 110.5
[[/math]]
Let S denote the aggregate distribution of retained claims.
[[math]]
\begin{aligned}
&\operatorname{E}[ S ] = \operatorname{E}[ N ] \operatorname{E}[ X \wedge 500] = 20(110.5) = 2210 \\
&\operatorname{E}[ S ] = \operatorname{E}[ N ]\operatorname{E}[ X \wedge 500] + \operatorname{E}[ ( X \wedge 500)^ 2 )\operatorname{E}[ N ] = 20(26,189) = 523, 780
\end{aligned}
[[/math]]
The 90th percentile of [math]S[/math] is [math]2210 + 1.282 \sqrt{523,780} = 3137.82.[/math]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.