A central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty. The starting point of our model is Hertig's log-normal chain-ladder

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... el. We embed this multiplicative claims reserving model into a multivariate log-normal framework. This multivariate framework is chosen such that we can simultaneously model several claims run-off triangles (subportfolios). In this model we can choose any correlation structure between the sub-portfolios and also within the sub-portfolios. Parameter uncertainty is modelled with a multivariate Gaussian prior distribution (which is a conjugate prior to the multivariate log-normal distribution, see Bü hlmann & Gisler (2005) ). This combination then allows to give a closed form solution for the claims reserving problem. Moreover, it allows to derive closed form confidence bounds which, at the same time, study process uncertainty and parameter uncertainty. These results are then used to study sensitivities and, moreover, they can be used to calibrate correlation estimates for solvency purposes. Michael Merz, Mario V. Wü thrich, Enkelejd Hashorva