Erlangian Approximations for Finitehorizon Ruin Probabilities
Sören Asmussen, Florian Avram and Miguel Usabel
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2001
ISSN 14039338

Abstract:

For the CramérLundberg risk model with phasetype claims, it is shown
that the probability of ruin before an independent phasetype time H
coincides with the ruin probability in a certain Markovian fluid model
and therefore has an matrixexponential form. When H is exponential,
this yields in particular a probabilistic interpretation of a recent result
of Avram & Usabel. When H is Erlang, the matrix algebra takes
a simple recursive form, and fixing the mean of H at T and
letting the number of stages go to infinity yields a quick approximation
procedure for the probability of ruin before time T. Numerical examples
are given, including a combination with extrapolation.



