Multivariate Cramér-Lundberg, including Gerber-Shiu metrics

This talk will be given by Prof. dr. M.R.H. (Michel) Mandjes (University of Amsterdam)


In this talk I'll focus on a multivariate variant of the conventional Cramér-Lundberg model. Imposing an ordering condition on the individual net cumulative claim processes, it turns out that the distribution of the joint running maximum can be derived, which can be used to evaluate ruin probabilities in a multivariate context. I start by analyzing the bivariate case, to then extend the reasoning to the higher-dimensional setting. The method relied upon uses the Kolmogorov forward equations underlying the associated queueing process. The solution reveals a so-called quasi-product form structure. We also point out how the results from this section can be translated into corresponding results for tandem queueing networks.

I conclude the talk by presenting an intricate analysis of the corresponding multivariate Gerber-Shiu metrics (covering ruin times, undershoots, and overshoots).

Joint work with Onno Boxma (Eindhoven)


Contact: if you are interested in joining this talk, please email Lanpeng Ji ( or Konstantinos Dareiotis ( for the Zoom link.