Limit theorems for discounted convergent perpetuities
Limit theorems for discounted convergent perpetuities
Let (ξ1,η1), (ξ2,η2),… be independent identically distributed R2-valued random vectors. We prove a strong law of large numbers, a functional central limit theorem and a law of the iterated logarithm for the convergent perpetuities ∑k≥0bξ1+…+ξkη k+1 as b→1−. Under the standard actuarial interpretation, these results correspond to the situation when …