Robust Fundamental Theorem for Continuous Processes

Abstract

We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\mathrm{NA}}_1(\mathcal{P})$ of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: ${\mathrm{NA}}_1(\mathcal{P})$ holds if and only if every $P\in \mathcal{P}$ admits a martingale measure which is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.

Forthcoming in 'Mathematical Finance'

References in corpus (4)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• A model-free version of the fundamental theorem of asset pricing and the super-replication theorem
• Martingale optimal transport in the Skorokhod space
• Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty

Cited by in corpus (1)

• On robust pricing-hedging duality in continuous time