Mathematical Finance and Stochastic Seminar by Tomasz R. Bielecki: Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Speaker: Tomasz R. Bielecki, professor of applied mathematics, Illinois InstituteTech
Title: Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Abstract:
Marked Hawkes processes are a class of marked point processes that exhibit self/mutual exciting and/or self/mutual inhibiting properties. Because of that they find numerous applications to modeling of dynamical random phenomena in the areas ranging from seismology to epidemiology, to finance, to neurology, to cybersecurity, to name just a few. A related class of processes are the compound marked Hawkes processes useful in particular for applications in (cyber-)insurance. We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement to those presented earlier in the literature. As an example, we provide an application to analysis of time limit of an insurance ruin process.
Stochastic Analysis