A new aspect of a risk process and its statistical inference

Yasutaka Shimizu

doi:10.1016/j.insmatheco.2008.10.002

A new aspect of a risk process and its statistical inference

Yasutaka Shimizu

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	70-77
Number of pages	8
Journal	Insurance: Mathematics and Economics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1016/j.insmatheco.2008.10.002
Publication status	Published - 2009 Feb
Externally published	Yes

Keywords

Adjustment coefficients
Diffusion perturbations
Discrete observations
Risk process
Statistical inference

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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title = "A new aspect of a risk process and its statistical inference",

abstract = "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.",

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note = "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.",

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