Section: New Results

Ruin probabilities

Participants : Georg Regensburger [correspondent] , Hansjörg Albrecher [Univ. Lausanne] , Corina Constantinescu [Univ. Lausanne] , Zbigniew Palmowski [Univ. Wroclaw] , Markus Rosenkranz [Univ. Kent] .

In a cooperation with Hansjörg Albrecher, Corina Constantinescu (both University of Lausanne), Zbigniew Palmowski (University of Wroclaw), and Markus Rosenkranz (University of Kent), we developed a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients and the corresponding Green's operators (integral operators), generalizing the approach from [99] . We obtain also closed-form solutions for more specific functions in the compound Poisson risk model.