Discover how the Dutch Book Theorem reveals profit opportunities in betting and finance when probabilities are misjudged.

This is a preview. Log in through your library . Abstract A simple proof of Wiener's multiparameter ergodic theorem is given in this paper. At the same time it is shown that two of the hypotheses of ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

We live in a world where a lot of things seem to happen by pure chance, from winning the Lotto to losing your car keys. But the truth is, the likelihood of many everyday things happening is heavily ...

Observing, gathering knowledge and making predictions are the foundations of the scientific process. The accuracy of our predictions depends on the quality of our present knowledge and accuracy of our ...

In science, progress is possible. In fact, if one believes in Bayes' theorem, scientific progress is inevitable as predictions are made and as beliefs are tested and refined. ~ Nate Silver If the ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...