The Maintenance Properties of nth Stop-Loss Order

This paper generalized the concept of stop-loss transforms to the nth stop-loss transforms. Some useful properties of the nth stop-loss transforms were discovered and a recursion formula for the nth stop-loss transforms was established. Also, the maintenance properties of the nth stop-loss order under convolution and compound operations were proved.

Keywords: classical risk model, homogeneous Poisson processes, stop-loss transform, stoploss order.