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The joint density function of three characteristics and the Gerber-Shiu discounted penalty function for the spectrally negative Levy process. (English) Zbl 1199.91095

Summary: The spectrally negative Lévy process starting at \(u (\geqslant 0)\) (namely the Lévy process with no positive jumps) is regarded as the generalized risk model and the joint density function of three characteristics: the time of ruin, the surpluses immediately before and at ruin is obtained. Using the derived results and \(\int^\infty_0\text{e}^{-\delta t}g_t (x)\text{d}t\) where \(g_t (x)\) is supposed to be the density function of the process at time \(t\), the Gerber-Shiu discounted penalty function for the spectrally negative Lévy process is proposed.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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