1
$\begingroup$

Given a Panjer Recursion set up, with the usual properties, and supposing now that $N$ has a Poisson distribution with mean $\lambda$.

How can we derive a recursion for $E(S^k)$ where $S$ be the total amount claimed in a year.

Additional background: Consider the total amount claimed in a year on a particular risk where the number of claims $N$ has $P(N = n) = P(n)$, $n = 0, 1, 2, \dots,$ and where claims are independent and identically distributed random variables $X_1, X_2, \dots$ independent of $N$. Suppose also that the claim sizes are positive and discrete with $P(X_1 = j) = f(j)$.

  • 0
    Hey Sam! The question starts by asking a proof of the Panjer recursion. It then tells to formulate using Panjer Recursion, a recursion for E(S^k). And then evaluate E(s), Var(s) and Skewness.2012-03-25

0 Answers 0