A note on limiting distribution for jumps of Lévy insurance risk model

• Published in: Journal of the Korean Statistical Society Vol. 40; no. 1; pp. 93 - 98
• Main Author: Park, Hyun Suk
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.03.2011; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Convolution equivalent distributions; Log-normal processes; Lévy insurance risk process; Non-Cramér condition; Quintuple law; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; secondary; Non-Cramér condition; Lévy insurance risk process; Convolution equivalent distributions; Quintuple law; Log-normal processes; primary; secondary 60G51; primary 91B30
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2010.07.001

Results of Doney and Kyprianou (2006) and Park and Maller (2008) for asymptotic overshoot and undershoot distributions in the class of a general Lévy process with convolution equivalent measures are used to obtain the limiting distribution of the maximum process before ruin, the undershoot immediately before ruin and the overshoot at ruin, associated with the ruin time. It allows us to study estimation and derivation of limiting distribution extensions for jumps when a ruin occurs. Numerical study of finite sample versions are given for specific illustrations of the limiting distributions.