Simulation methods in ruin models with non-linear dividend barriers

Authors:
Hansjörg Albrecher;Reinhold Kainhofer;Robert F. Tichy
Affiliations:
Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria
Venue:
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
Year:
2003

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Abstract

In this paper, a collective risk reserve process of an insurance portfolio characterized by a homogeneous Poisson claim number process, a constant premium flow and independent and identically distributed claims is considered. In the presence of a non-linear dividend barrier strategy and interest on the free reserve we derive equations for the probability of ruin and the expected present value of dividend payments which give rise to several numerical number-theoretic solution techniques. For various claim size distributions and a parabolic barrier numerical tests and comparisons of these techniques are performed. In particular, the efficiency gain obtained by implementing low-discrepancy sequences instead of pseudo-random sequences is investigated.