Ruin probabilities via local adjustment coefficients
- 1 September 1995
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 32 (3) , 736-755
- https://doi.org/10.2307/3215126
Abstract
Let ψ(u) be the ruin probability in a risk process with initial reserve u, Poisson arrival rate β, claim size distribution B and premium rate p(x) at level x of the reserve. Let y(x) be the non-zero solution of the local Lundberg equation . It is shown that is non-decreasing and that log ψ(u) ≈ –I(u) in a slow Markov walk limit. Though the results and conditions are of large deviations type, the proofs are elementary and utilize piecewise comparisons with standard risk processes with a constant p. Also simulation via importance sampling using local exponential change of measure defined in terms of the γ(x) is discussed and some numerical results are presented.Keywords
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