equivalence of absence of arbitrage, the existence of a positive linear pricing rule, and the existence of an optimum for some … preferences, and solving them for probabilities gives us beliefs. We look at two popular asset pricing models, the CAPM and the … APT, as well as complete-markets pricing. In the case of the CAPM, the first-order conditions link nicely to the …

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to … the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities … anymore. We use convex optimization, and the conic property of this region to characterize the "no-arbitrage" principle in …