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# Finite and in ! nite time ruin probabilities in a stochastic economic environment

@inproceedings{Nyrhinen2001FiniteAI, title={Finite and in ! nite time ruin probabilities in a stochastic economic environment}, author={Harri Nyrhinen}, year={2001} }

- Published 2001

Let (A1; B1; L1); (A2; B2; L2); : : : be a sequence of independent and identically distributed random vectors. For n ∈ N, denote Yn = B1 + A1B2 + A1A2B3 + · · ·+ A1 · · ·An−1Bn + A1 · · ·AnLn: For M ¿ 0, de!ne the time of ruin by TM=inf{n |Yn ¿M} (TM=+∞, if Yn6M for n=1; 2; : : :). We are interested in the ruin probabilities for large M . Our objective is to give reasons for the crude estimates P(TM6x logM) ≈ M−R(x) and P(TM ¡∞) ≈ M−w where x ¿ 0 is !xed and R(x) and w are positive parameters… CONTINUE READING

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