Titlebook: Market-Consistent Prices; An Introduction to A Pablo Koch-Medina,Cosimo Munari Textbook 2020 Springer Nature Switzerland AG 2020 arbitrage

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Fundamental Theorem of Asset Pricing,al. The first version of the Fundamental Theorem of Asset Pricing states that the absence of arbitrage opportunities is equivalent to the existence of a . from the marketed space to the entire payoff space. Each of these extensions can be viewed as a hypothetical pricing rule in a complete arbitrage

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Market-Consistent Prices for General Payoffs,icable payoffs to general, not necessarily replicable, payoffs. Because this extension relies on the strict positivity of the pricing functional, we focus exclusively on arbitrage-free markets. We show that, given the market environment, the set of prices at which rational buyers and sellers will co

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Random Variables: Information and Measurability, sample space as a way of modeling the granularity of the information we may obtain about the outcome of a random experiment. The highest granularity corresponds to full information and the lowest to no information. Intermediate granularity levels correspond to partial information. A key concept rel

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Conditional Probabilities and Expectations,ch we receive information comes in the form of a partition of the underlying sample space and only allows us to evaluate random variables that are measurable with respect to that partition. In this chapter we investigate how the assessment of probabilities and, hence, expectations is affected by the

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Extensions of Conditional Linear Functionals, particular, we obtain a conditional version of the Riesz Representation Theorem in which conditional expectations play the role of expectations. We pay special attention to conditional linear functionals that are strictly positive because the corresponding extension and representation results play

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Fundamental Theorem of Asset Pricing, existence of a . of the pricing functionals. In line with the interpretation provided in the context of a single-period model, each of these extensions can be viewed as a hypothetical pricing rule in a complete market under which the original basic securities maintain their prices. The other versio