# Dutch Book Theorem

## DEFINITION of 'Dutch Book Theorem'

A type of probability theory that postulates that profit opportunities will arise when inconsistent probabilities are assumed in a given context and are in violation of the Bayesian approximation. The assumed probabilities can be rooted in behavioral finance, and will be a direct result of human error in calculating the probability that an event will occur.

## BREAKING DOWN 'Dutch Book Theorem'

In other words, the theory states that when an inaccurate assumption is made about the likelihood that an event will occur, a profit opportunity will arise for an intermediary.

For example, assume there is one insurance company and 100 people in a given house insurance market. If the insurance company predicts that the probability that a homeowner will need insurance is 5%, but all homeowners predict that the probability of needing insurance is 10%, then the insurance company can charge more for home insurance. This is because the insurance company knows people will pay more for insurance than what will be needed. The profit comes from the difference between premiums charged for insurance and the costs the insurance company incurs through settling insurance claims.