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We study the Fundamental Theorem of Asset Pricing for a general financial market under Knightian Uncertainty. We adopt a functional analytic approach which require neither specific assumptions on the class of priors $mathcal{P}$ nor on the structure of the state space. Several aspects of modeling under Knightian Uncertainty are considered and analyzed. We show the need for a suitable adaptation of the notion of No Free Lunch with Vanishing Risk and discuss its relation to the choice of an appropriate filtration. In an abstract setup, we show that absence of arbitrage is equivalent to the existence of emph{approximate} martingale measures sharing the same polar set of $mathcal{P}$. We then specialize the results to a discrete-time framework in order to obtain true martingale measures.
We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian Uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive
In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class $mathcal{S}$ of significant sets, which we call Arbitrage de la cl
We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free Variational Autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven model
The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of (idealized) markets. The paper addresses the following basic question: can o
We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agents preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlin