TY - JOUR
T1 - Estimation of the expected discounted penalty function for Lévy insurance risks
AU - Shimizu, Y.
N1 - Funding Information:
The author expresses his sincere thanks to an anonymous referee for his/her comments and instructions with the careful reading. Moreover, the author would like to thank Prof. José Garrido, who gave some useful comments on an earlier version of this paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 2009– 2011, no. 21740073, and Japan Science and Technology Agency, CREST.
PY - 2011/6
Y1 - 2011/6
N2 - We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.
AB - We consider a generalized risk process which consists of a subordinator plus a spectrally negative Lévy process. Our interest is to estimate the expected discounted penalty function (EDPF) from a set of data which is practical in the insurance framework. We construct an empirical type estimator of the Laplace transform of the EDPF and obtain it by a regularized Laplace inversion. The asymptotic behavior of the estimator under a high frequency assumption is investigated.
KW - ISE-consistency
KW - Lévy risk process
KW - discrete observations
KW - expected discounted penalty function
KW - regularized Laplace inversion
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U2 - 10.3103/S1066530711020037
DO - 10.3103/S1066530711020037
M3 - Article
AN - SCOPUS:84859573976
SN - 1066-5307
VL - 20
SP - 125
EP - 149
JO - Mathematical Methods of Statistics
JF - Mathematical Methods of Statistics
IS - 2
ER -