### 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 |
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Pages (from-to) | 70-77 |

Number of pages | 8 |

Journal | Insurance: Mathematics and Economics |

Volume | 44 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 Feb |

Externally published | Yes |

### Fingerprint

### Keywords

- Adjustment coefficients
- Diffusion perturbations
- Discrete observations
- Risk process
- Statistical inference

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Economics and Econometrics
- Statistics and Probability

### Cite this

**A new aspect of a risk process and its statistical inference.** / Shimizu, Yasutaka.

Research output: Contribution to journal › Article

*Insurance: Mathematics and Economics*, vol. 44, no. 1, pp. 70-77. https://doi.org/10.1016/j.insmatheco.2008.10.002

}

TY - JOUR

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

AU - Shimizu, Yasutaka

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

UR - http://www.scopus.com/inward/record.url?scp=58249092618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58249092618&partnerID=8YFLogxK

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 -