Some Expressions of a Generalized Version of the Expected Time in the Red and the Expected Area in Red

Abstract

In this paper, we study a generalized version of the expected time in the red and the expected area in red introduced in Loisel ( 2005). We derive some expressions for this risk measure both in light tailed and heavy tailed cases for general risk processes. Then, some further expressions are obtained for Lévy processes together with an upper bound in the light-tailed case and an additional result for large initial capitals in the subexponential case.