On the distribution of the duration of negative surplus

Abstract

In the classical risk model we allow the surplus process to continue if the surplus falls below zero. We consider the distributions of the duration of a single period of negative surplus and of the total duration of negative surplus. We derive explicit results where possible and show how to approximate these distributions through the use of a discrete time risk model.

Key words:

• Ruin theory
• negative surplus
• severity of ruin
• failure rate
• recursive calculation
• discrete time model