Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz iew\c{e}g{\l}owski, Anatoliy Swishchuk
TL;DR
This paper establishes functional laws of large numbers for marked Hawkes processes and their compound variants, extending existing results and applying them to insurance ruin time analysis.
Contribution
It introduces new functional laws of large numbers for a broad class of marked Hawkes processes with general marks, complementing prior research.
Findings
Proves functional laws of large numbers for marked Hawkes processes.
Provides an application to insurance ruin time analysis.
Extends theoretical understanding of marked Hawkes processes.
Abstract
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 previously in the literature. As an example we provide an application to analysis of time limit of an insurance ruin process.
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