We consider a model of an insurance company investing its reserve into a risky asset whose price follows a geometric Lévy process. We show that the nonruin probability is a viscosity solution of a second order integro-differential equation and prove a uniqueness theorem for the latter.
We prove results on an exact small deviation asymptotics in L_2-norm for Matérn processes with arbitrary natural index and on logarithmic asymptotics for Matérn processes and fields with arbitrary indexes.
This paper is focused on stability conditions of a multi-server queueing system with regenerative input flow where a random number of servers is simultaneously required for each customer and each server's completion time is constant. It turns out that the stability condition depends on the rate of the input flow and not on its structure.