This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a...

In a classical risk model under constant interest force, we study the probability that the surplus of an insurance company reaches an upper barrier before a lower barrier. We define this probability as win-first probability. Borrowing ideas from life-insurance theory, hazard rates of the maximum...

The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly non-continuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these...

This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a...