Number of claims and ruin time for a refracted risk process
  In this paper, we consider a classical risk model refracted at given level. We give an explicit expression for the joint density of the ruin time and the cumulative number of claims counted up to ruin time. The proof is based on solving some integro-differential equations and employing the Lagrange's Expansion Theorem. 
Yanhong Li, Zbigniew Palmowski, Chunming Zhao, Chunsheng Zhang
math.PR