Arbitrage and the Dutch Book Theorem

Journal of Philosophical Research 22:477-482 (1997)
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Philosophical writing on probability theory includes a great many articles discussing relationships between rational behavior and an agent’s susceptibility to betting contexts where an overall loss is mathematically inevitable. What the dutch book theorem establishes is that this kind of susceptibility is a consequence of having betting ratios that are in violation of the Kolmogorov probability axioms. In this article it is noted that a general result to rule out arbitrage can be shown to yield the dutch book theorem as a special case. A formal framework is set forth to handle marketplace transactions involving contractual arrangements; and, within that framework, necessary and sufficient conditions are given for ruling out arbitrage. It is then shown that these conditions entail that pricing functions associated with particular kinds of betting contracts must turn out to be probability functions



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