The Cramer-Lundberg Approximation: A New Approach
The well-known Cramer-Lundberg approximation says that for large u, the ultimate ruin probability w(u) satisfies w(u)~Ce-Ru, where u is the initial reserve, R is the adjustment coefficient and C is a positive constant. Our aim in this work is to present a new expression for C in the classical perturbed risk process and to extend this expression in two cases: 1) possibly negative claims and 2) an infinite number of claims on finite time intervals.
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