The conjectures of Embrechts and Goldie

2015/11/04 by Toshiro Watanabe, Watanabe, Toshiro
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E99 #60G50 #62E20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #math.PR #msc:60E99 #msc:60G50 #msc:62E20

paper · pdf · doi:10.48550/arxiv.1511.01246

15 pages

arxiv created 2015/11/04 · openalex publication_date 2015/11/04 · arxiv updated 2015/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. Moreover, two sufficient conditions for the closure under convolution roots of the class of convolution equivalent distributions are given.

Related

• Two non-closure properties on the class of subexponential densities
• Some positive conclusions related to the Embrechts-Goldie' conjecture
• On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)
• On convolution closure properties of subexponentiality approaching from densities
• Two hypotheses on the exponential class in the class of O-subexponential infinitely divisible distributions