A0946
Title: What is the average surplus before ruin?
Authors: Eric Chi Kin Cheung - UNSW Sydney (Australia)
Runhuan Feng - University of Illinois at Urbana-Champaign (United States)
Haibo Liu - Purdue University (United States)
Jae-Kyung Woo - UNSW Sydney (Australia) [presenting]
Abstract: The aim 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, it is shown that the moments of the average surplus can be obtained by integrating the discounted moments of the area under the sample 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). Explicit formulas are also provided for the case where the claim amounts are a combination of exponentials.
