We present mathematical results allowing one to evaluate the moments of order 1 and 2 of the cedent's share in the framework of reinsurance treaties based on ordered claim sizes. These results consist of closed analytical formulas that do not involve any approximation procedure. This is...

Using classical results on the projective limit of a sequence of subsets, we show the existence of martingale selectors for a multivalued martingale (and supermartingale) with closed values in a separable Banach space X. The existence of L1(X)-bounded or uniformly integrable martingale selectors...

We first establish a general version of the Birkhoff Ergodic Theorem for quasi-integrable extended real-valued random variables without assuming ergodicity. The key argument involves the Poincaré Recurrence Theorem. Our extension of the Birkhoff Ergodic Theorem is also shown to hold for...