TY - JOUR
T1 - Gerber-Shiu analysis in the compound Poisson model with constant inter-observation times
AU - Xie, Jiayi
AU - Yu, Wenguang
AU - Zhang, Zhimin
AU - Cui, Zhenyu
N1 - Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.
PY - 2023/4/1
Y1 - 2023/4/1
N2 - In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.
AB - In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.
KW - Compound Poisson model
KW - Gerber-Shiu function
KW - Laguerre series expansion
KW - Periodic observation
UR - http://www.scopus.com/inward/record.url?scp=85152620419&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85152620419&partnerID=8YFLogxK
U2 - 10.1017/S0269964822000092
DO - 10.1017/S0269964822000092
M3 - Article
AN - SCOPUS:85152620419
SN - 0269-9648
VL - 37
SP - 324
EP - 356
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 2
ER -