Asymptotic Consistency and Inconsistency of the Chain Ladder
Asymptotic Consistency and Inconsistency of the Chain Ladder
Asymptotic Consistency and Inconsistency of the Chain Ladder
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<strong>Consistency</strong>Denote D (n)j= {C i,k : k ≤ j, i ≤ n − j + 1} <strong>and</strong>D j = {C i,k : k ≤ j, i ∈ N}. Then (i)–(iv) are equivalent:(i)̂f (n) [P Dj ]-a.s.j−−−−−−→ f j, [P]-a.s.;n→∞(ii)(iii)(iv)̂f (n)jn−j∑i=1̂f (n)jP D(n)j−−−→n→∞ f j, [P]-a.s.;L 2(P (n) Dj)−−−−−−−→ f j, [P]-a.s.;n→∞C i,j −−−→n→∞∞, [P]-a.s.
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