Title:  Excursion theory for spectrally negative Levy processes and its applications 
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Abstract: Levy processes are stochastic processes with stationary independent increments. We call it spectrally negative if it only allows negative jumps. By excursion theory the spectrally negative Levy process can be identified as a nice path-valued process. Such an identification is very useful in studying exit related properties for the Levy process. In this talk we will also introduce some applications of excursion theory to the Levy risk processes for insurance.