Compound Poisson processes. Interestnig properties

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I'm currently finishing my bachleor's studies and have to pick a topic for my bachelor's thesis. I'm leaning towards analysing the compound Poisson process, but since the thesis should be about 30 pages I don't thing only proving basic results will suffice. What would be an interesting property of the process I could study in my thesis? Possibly something to do with finance, and if you give any suggestions I would appreciate a refference to the material that covers said suggested topic.