  We use a logical device called the Dutch Book to establish epistemic
confidence, defined as the sense of confidence \emph{in an observed} confidence
interval. This epistemic property is unavailable -- or even denied -- in
orthodox frequentist inference. In financial markets, including the betting
market, the Dutch Book is also known as arbitrage or risk-free profitable
transaction. A numerical confidence is deemed epistemic if its use as a betting
price is protected from the Dutch Book by an external agent. Theoretically, to
construct the Dutch Book, the agent must exploit unused information available
in any relevant subset. Pawitan and Lee (2021) showed that confidence is an
extended likelihood, and the likelihood principle states that the likelihood
contains all the information in the data, hence leaving no relevant subset.
Intuitively, this implies that confidence associated with the full likelihood
is protected from the Dutch Book, and hence is epistemic. Our aim is to provide
the theoretical support for this intuitive notion.
