  We propose a recursive method for the computation of the cumulants of
self-exciting point processes of Hawkes type, based on standard combinatorial
tools such as Bell polynomials. This closed-form approach is easier to
implement on higher-order cumulants in comparison with existing methods based
on differential equations, tree enumeration or martingale arguments. The
results are corroborated by Monte Carlo simulations, and also apply to the
computation of joint cumulants generated by multidimensional self-exciting
processes.
