TY - JOUR

T1 - A new aspect of a risk process and its statistical inference

AU - Shimizu, Yasutaka

N1 - Funding Information:
The author expresses many thanks to the anonymous referees for their helpful comments. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), no. 19740049, 2007.

PY - 2009/2

Y1 - 2009/2

N2 - We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the process does not necessarily correspond to the each claim size. Therefore our risk process is different from the traditional risk process. We cannot directly observe each jump size because of discrete observations. Our goal is to estimate the adjustment coefficient of our risk process from discrete observations.

AB - We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the process does not necessarily correspond to the each claim size. Therefore our risk process is different from the traditional risk process. We cannot directly observe each jump size because of discrete observations. Our goal is to estimate the adjustment coefficient of our risk process from discrete observations.

KW - Adjustment coefficients

KW - Diffusion perturbations

KW - Discrete observations

KW - Risk process

KW - Statistical inference

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U2 - 10.1016/j.insmatheco.2008.10.002

DO - 10.1016/j.insmatheco.2008.10.002

M3 - Article

AN - SCOPUS:58249092618

VL - 44

SP - 70

EP - 77

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 1

ER -