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Pricing without martingale measure
Multi angle
Authors : Carassus, Laurence (Author of the conference)
CIRM (Publisher )
49N15 - Duality theory
60G42 - Martingales with discrete parameter
90C15 - Stochastic programming
91G10 - Portfolio theory
CIRM (Publisher )
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Abstract :
For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and biconjugate.
This naturally leads to a weak condition of absence of arbitrage opportunity, called Absence of Immediate Profit (AIP), which asserts that the price of the zero claim should be zero. We study the link between (AIP), (NA) and the no-free lunch condition. We show in a one step model that, under (AIP), the super-hedging cost is just the payoff's concave envelop and that (AIP) is equivalent to the non-negativity of the super-hedging prices of some call option.
In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option. We also give some numerical illustrations.
Keywords : financial market models; super-hedging prices; no-arbitrage condition; conditional support; essential suprenum
MSC Codes : This naturally leads to a weak condition of absence of arbitrage opportunity, called Absence of Immediate Profit (AIP), which asserts that the price of the zero claim should be zero. We study the link between (AIP), (NA) and the no-free lunch condition. We show in a one step model that, under (AIP), the super-hedging cost is just the payoff's concave envelop and that (AIP) is equivalent to the non-negativity of the super-hedging prices of some call option.
In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option. We also give some numerical illustrations.
Keywords : financial market models; super-hedging prices; no-arbitrage condition; conditional support; essential suprenum
49N15 - Duality theory
60G42 - Martingales with discrete parameter
90C15 - Stochastic programming
91G10 - Portfolio theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/09/2018 Conference Date : 06/09/2018 Subseries : Research talks arXiv category : Mathematical Finance Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:33:25 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-09-06_Carassus.mp4 
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Information on the Event
Event Title : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financièresEvent Organizers : Callegaro, Giorgia ; Jeanblanc, Monique ; Lépinette, Emmanuel ; Molchanov, Ilya ; Schweizer, Martin ; Touzi, Nizar Dates : 03/09/2018 - 07/09/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1816.html
Citation Data
DOI : 10.24350/CIRM.V.19444203Cite this video as: Carassus, Laurence (2018). Pricing without martingale measure. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19444203 URI : http://dx.doi.org/10.24350/CIRM.V.19444203 |
See Also
- [Multi angle] Set-valued risk measures of non-convex portfolios / Author of the conference Molchanov, Ilya.
- [Multi angle] Discounting invariant FTAP for large financial markets / Author of the conference Balint, Daniel.
- [Multi angle] From multivariate quantiles to set-valued risk measures: a set optimization - approach to financial models with frictions / Author of the conference Hamel, Andreas H..
- [Post-edited] Approximation and calibration of laws of solutions to stochastic differential equations / Author of the conference Bion-Nadal, Jocelyne.
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