2023 Australasian Actuarial Education and Research Symposium

Jae Kyung Woo

UNSW Sydney

What is the average surplus before ruin?

This is joint work with E. Cheung, R. Feng, H. Liu

Our goal is to study the moments of the average surplus before ruin in a renewal risk process with a general interclaim time distribution. The average surplus before ruin is calculated as the area under the sample path divided by the ruin time, which provides a new ruin quantity of interest. However, the traditional approach of conditioning on the first claim event is no longer feasible because the ruin time appears in the denominator. To circumvent this, we show that the moments of the average surplus can be obtained by integrating the discounted moments of the area under the sample path with respect to the force of interest. These discounted moments can then be determined using a moment-based discounted density similar to the one in Cheung (2013). We also provide explicit formulas for the case where the claim amounts are a combination of exponentials.