Robust Fundamental Theorem for Continuous Processes

Sara Biagini (1) , Bruno Bouchard (2) , Constantinos Kardaras (3) , Marcel Nutz (4)

1 University of Pisa - Università di Pisa
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 LSE - London School of Economics and Political Science
4 Dept. of Mathematics

We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA1(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: NA1(P) holds if and only if every P ∈ 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.

Mots clés: Superhedging duality; Nondominated Model AMS 2010 Subject Classification 91B25; Arbitrage of the First Kind; Fundamental Theorem of Asset Pricing; 60G44; 93E20

Domaines: Probabilités [math.PR]; Économie et finance quantitative [q-fin]

Sara Biagini, Bruno Bouchard, Constantinos Kardaras, Marcel Nutz. Robust Fundamental Theorem for Continuous Processes. Mathematical Finance, 2017, 27 (4), pp.963-987. ⟨10.1111/mafi.12110⟩. ⟨hal-01076062⟩