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 NA 1(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: NA 1(P) holds if and only if every P∈P admits a martingale measure that 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.

Robust fundamental theorem for continuous processes / Biagini, Sara; Bouchard, Bruno; Kardaras, Constantinos; Nutz, Marcel. - In: MATHEMATICAL FINANCE. - ISSN 0960-1627. - 27:4(2017), pp. 963-987. [10.1111/mafi.12110]

Robust fundamental theorem for continuous processes

BIAGINI, SARA;
2017

Abstract

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 NA 1(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: NA 1(P) holds if and only if every P∈P admits a martingale measure that 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.
Arbitrage of the first kind; Fundamental theorem of asset pricing; Nondominated model; Superhedging duality; Applied Mathematics; Finance; Accounting; Economics and Econometrics; Social Sciences (miscellaneous)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/171320
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