General Multivariate Hawkes Processes and Induced Population Processes: exact results and large deviations

Speaker: Prof. Michel Mandjes (Leiden University, the Netherlands)

Joint work with Raviar Karim and Roger Laeven (both University of Amsterdam), and Onno Boxma (Eindhoven University of Technology).

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Date	Time	Venue	Access
Nov. 20	14:00 (Shanghai time, CST)	R1210， SIMIS	Zoom Meeting ID:825 7461 8716 Passcode: SIMIS

Abstract

Among multivariate point processes, the class of Hawkes processes, or mutually exciting processes, provides a natural contender for modeling contagion phenomena. In this talk I’ll discuss multivariate population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals.

The first class of results concerns the identification of the time-dependent joint probability distribution, allowing for general intensity decay functions, general intensity jumps, and general sojourn times, in terms of a fixed-point representation.

The second class of results focuses on risk processes driven by multivariate Hawkes arrivals. The main results are (i) a large deviations principle for the cumulative claim process in the light-tailed regime, (ii) the identification of the decay rate of the ruin probability, and (iii) an importance sampling based efficient simulation procedure to estimate rare events.