| Expectation and variance of the total claim amount in the renewal model |
| Written by theoretic |
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In the renewal model, if EW\ = A-1 and EX\ are finite, ES(t) lim = \EX\, t^oo t and if var(W\) and var(Xi) are finite, var(S(t)) г , о-, lim = A var(Ai)+var( И) А М) . t^oo t In the Cramer-Lundberg model these limit relations degenerate to identities for every t > 0: ES(t)=\tEX\ and var(S(t)) = At E(X2). The message of these results is that in the renewal model both the expectation and the variance of the total claim amount grow roughly linearly as a function oft. This is important information which can be used to give a rule of thumb about how much premium has to be charged for covering the losses S(t): the premium should increase roughly linearly and with a slope larger than A EX\. In Section 3.1.3 we will consider some of the classical premium calculation principles and there we will see that this rule of thumb is indeed quite valuable. |