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...

The new prudential standards, Solvency II, consider the question of controling of insurer and reinsurer’s solvency. In this thesis, we’ve proposed technical solution for solvency capital assessment to keep ruin’s probability under the target of 0.5% aimed by the Solvency II project in...

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 claimsizes. These results consist of closed analytical formulas that do not involve any approximation procedure. This is...