an:06410267
Zbl 1310.60058
Yin, Chuancun; Yuen, Kam C.
Exact joint laws associated with spectrally negative L??vy processes and applications to insurance risk theory
EN
Front. Math. China 9, No. 6, 1453-1471 (2014).
00337389
2014
j
60G51 60G50 60J75 91B30
spectrally negative L??vy processes; fluctuation identity; generalized Dickson's formula; scale function; occupation time; insurance risk theory
Summary: We consider the spectrally negative L??vy processes and determine the joint laws for quantities such as the first and last passage times over a fixed level, the overshoots and undershoots at first passage, the minimum, the maximum, and the duration of negative values. We apply our results to insurance risk theory to find an explicit expression for the generalized expected discounted penalty function in terms of scale functions. Furthermore, a new expression for the generalized Dickson's formula is provided.