![]() He showed it implied the existence of finitely-additive beliefs over events and linear utilities over states of nature. Savage has a result about any procedure for making decisions under uncertainty that satisfied a set of reasonable-looking conditions including coherence. I had assumed the fact that the Dutch Book Theorem does not hold in finance was probably not a problem in real-world activity, but I am pretty certain that I was wrong. What I was hoping for was a general proof. I can show that in my specific case, there will arise cases where a Dutch Book can be constructed. Models like Black-Scholes, aside from being problem-ridden, are also Frequentist in construction. Less than one percent of finance articles are Bayesian and they usually cover side cases. ![]() ![]() Finance is almost purely a Frequentist discussion. That would except the case where the Bayesian and Frequentist solution map to the same answer.Īs to how do you apply coherence to Frequentist statistics, you don't. The exception would be where the Frequentist and the Bayesian results map to the same values everywhere.Ĭan someone cite a proof for me, or provide one as the general case? I have looked and failed to find one in the literature.ĮDIT Proof that if I were to gamble that $\mu\ge$ and construct the odds using a Frequentist method, then there would exist cases where a Dutch Book could be constructed. ![]() It is pretty easy to create examples of this fact. So, without proof or citation, I often see that the Coherence Principle by de Finetti does not hold with Frequentist statistics. ![]()
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