Tid: 11 oktober 1999 kl 1515-1700

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Alessandro Juri, Financial and Insurance Mathematics, Departement of Mathematics, ETH Zurich

Titel: Supermodular order and Lundberg exponent


In the actuarial literature we find models where in most of the cases the total claim amount at a given time that an insurance company has to face with is given by a compound process. For a wide class of such models a main result is that the infinite- and the finite-time ruin probabilities show an exponential decay in the initial capital. It is surprising that only a minor attention is given to multivariate processes, which may be used to describe the capital at a given time of insurance companies with more than one line of business, and to models where possible dependencies (e.g. between the claim sizes) are taken into account. It turns out that a special kind of stochastic order for probability measures on $\,(R^n,{\cal B}(R^n))$, the so called supermodular order, is an adequate tool for modelling dependencies. In this talk we shed some light on how to combine the well-known results for ruin probabilities in the univariate case and the techniques offered by the supermodular order to get results in the multivariate case. More precisely, we consider a multivariate risk process, where each component is a univariate risk process and we obtain a monotonicity result for the infinite- and finite-time Lundberg exponent of the sum component process. We also use the supermodular order to introduce a dependency structure in the underlying point process and again a monotonicity result is obtained.

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