On total claim amount for marked Poisson cluster models (CROSBI ID 262496)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Basrak, Bojan ; Wintenberger, Olivier ; Žugec, Petra
engleski
On total claim amount for marked Poisson cluster models
We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. The marks determine the size and other characteristics of the individual claims and potentially influence arrival rate of the future claims. We find sufficient conditions under which the total claim amount satisfies the central limit theorem or alternatively tends in distribution to an infinite variance stable random variable. We discuss several Poisson cluster models in detail, paying special attention to the marked Hawkes processes as our key example.
Poisson cluster processes ; limit theorems ; Hawkes process ; total claim amount ; central limit theorem ; stable random variables
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Podaci o izdanju
51 (2)
2019.
541-569
objavljeno
0001-8678
1475-6064
10.1017/apr.2019.15
Povezanost rada
Matematika