Asymptotic Consistency and Inconsistency of the Chain Ladder

Reasonable Estimatefor Reserves- nonsense estimate, e.g., ̂Ri = 10 6 or ̂R i = −1◮ why bad? the most precise estimate (in terms ofvariability) Var ̂R i = 0- unbiased estimate, i.e., E ̂R i = ER i , or conditionallyunbiased◮ firstly, introduce a model with assumptions, thenconstruct an estimate◮ have you ever heard of a reserving model withunbiased estimates of reserves?- consistent estimate (but where’s n ?)̂R i(stochastically)−−−−−−−−−→ R in→∞