Asymptotic behavior of the Gerber–Shiu discounted penalty function in the Erlang(2) risk process with subexponential claims

Abstract

We investigate the asymptotic behavior of the Gerber–Shiu discounted penalty function ɸ(u) = E(e−δT 1_{{T <∞}} | U(0) = u), where T denotes the time to ruin in the Erlang(2) risk process. We obtain an asymptotic expression for the discounted penalty function when claim sizes are subexponentially distributed.