exercise:A412453a8a: Difference between revisions

Latest revision as of 21:48, 24 July 2024

You are given the following:

Claim frequency and claim size are independent
Monthly claim frequency is Poisson distributed with mean 3
The claim size distribution depends on parameters [math]a,b[/math]: when [math]a \lt b [/math] the distribution is uniform on [math][a,b][/math] and when [math]a = b [/math] the claim size equals [math]b [/math] with probability 1.

If [math]S[/math] is the annual loss, determine the maximum of [math]\operatorname{E}[S^2]/\operatorname{E}[S]^2[/math] over all possible values a,b.

@@ Line 1: / Line 1: @@
-You are given the following about a risk:
+You are given the following:
 *Claim frequency and claim size are independent
 *Monthly claim frequency is Poisson distributed with mean 3
-*Claim size is uniformly distributed on [a,b]
+*The claim size distribution depends on parameters <math>a,b</math>: when <math>a < b </math> the distribution is uniform on <math>[a,b]</math> and when <math>a = b </math> the claim size equals <math>b </math> with probability 1.
-If <math>S</math> is an annual loss for the risk, determine the maximum of <math>\operatorname{E}[S^2]/\operatorname{E}[S]^2</math> over all possible values (a,b).
+If <math>S</math> is the annual loss, determine the maximum of <math>\operatorname{E}[S^2]/\operatorname{E}[S]^2</math> over all possible values a,b.
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