# A new aspect of a risk process and its statistical inference

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## 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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