In ruin theory, the conjecture given in De Vylder and Goovaerts (2000) is an open problem about the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability evaluated in the associated model with equalized claim amounts. In this paper we consider a weaker version of the conjecture and show that the integrals of the ruin probabilities with respect to the initial risk reserve are uniformly comparable.
"On the De Vylder and Goovaerts conjecture about ruin for equalized claims." J. Appl. Probab. 51 (3) 874 - 879, September 2014. https://doi.org/10.1239/jap/1409932679