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Pathwise or quasi-sure towards dynamic robust framework for pricing and hedging

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Post-edited
Authors : Obloj, Jan (Author of the conference)
CIRM (Publisher )

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robust pricing and hedging framework robust model superhedging price martingale measure FTAP pathwise vs quasi-sure pricing-hedging duality American options minimal superhedging concave envelop maximisation of utility of consumption information quantification statistical estimation of superhedging prices questions of the audience
Abstract : I discuss some recent developments related to the robust framework for pricing and hedging in discrete time. I introduce pointwise approach based on pathspace restrictions and compare it with the quasi-sure setting of Bouchard and Nutz (2015), and show that their versions of the Fundamental Theorem of Asset Pricing and the Pricing-Hedging duality may be deduced one from the other via a construction of a suitable set of paths which represents a given set of measures. I show that the setup with statically traded hedging instruments can be naturally lifted to a setup with only dynamically traded assets without changing the superhedging prices. This allows one to deduce, in particular, a pricing-hedging duality for American options. Subsequently, I focus on the superhedging problem and discuss the choice of a trading strategy amongst all feasible super-hedging strategies. First, I establish existence of a minimal superhedging strategy and characterise its value via a concave envelope construction. Then I introduce a secondary problem of maximisation of expected utility of consumption. Building on Nutz (2014) and Blanchard and Carassus (2017) I provide suitable assumptions under which an optimal strategy exists and is unique. Finally, I also explain how additional information can be seen as a further restriction of the pathspace. This allows one to quantify to value of such a new information. The talk is based on a number of recent works (see references) as well as ongoing research with Johannes Wiesel.

MSC Codes :
28A05 - Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
 49N15 - Duality theory
 60G40 - Stopping times; optimal stopping problems; gambling theory
 60G42 - Martingales with discrete parameter
 90C46 - Optimality conditions, duality
 91B70 - Stochastic models in economics
 91G20 - Derivative securities
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 17/11/2017
    Conference Date : 16/11/2017
    Subseries : Research talks
    arXiv category : Probability ; Mathematical Finance
    Mathematical Area(s) : Probability & Statistics ; Mathematics in Science & Technology ; Computer Science ; Analysis and its Applications ; Control Theory & Optimization
    Format : MP4 (.mp4) - HD
    Video Time : 00:41:12
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2017-11-16_Obloj.mp4
Information on the Event

Event Title : Advances in stochastic analysis for risk modeling / Avancées en analyse stochastique pour la modélisation des risques
Event Organizers : Bouchard, Bruno ; Cheridito, Patrick ; Schweizer, Martin ; Touzi, Nizar
Dates : 13/11/2017 - 17/11/2017
Event Year : 2017
Event URL : https://conferences.cirm-math.fr/1730.html

Citation Data

DOI : 10.24350/CIRM.V.19245603
Cite this video as: Obloj, Jan (2017). Pathwise or quasi-sure towards dynamic robust framework for pricing and hedging. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19245603
URI : http://dx.doi.org/10.24350/CIRM.V.19245603

See Also

Bibliography

  • Aksamit, A., Deng, S., Obloj, J., & Tan, X. (2017). Robust pricing-hedging duality for American options in discrete time financial markets. - https://arxiv.org/abs/1604.05517

  • Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., & Obloj, J. (2016). Pointwise Arbitrage Pricing Theory in Discrete Time. - https://arxiv.org/abs/1612.07618

  • Aksamit, A., Hou, Z., & Obloj, J. (2016). Robust framework for quantifying the value of information in pricing and hedging. - https://arxiv.org/abs/1605.02539


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