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Financial markets with volatility uncertainty

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  • Jörg Vorbrink

    (Institute of Mathematical Economics, Bielefeld University)

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    Abstract

    We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of G–expectation and its corresponding G–Brownian motion recently introduced by Peng (2007). Our financial market consists of a riskless asset and a risky stock with price process modeled by a geometric G–Brownian motion. We adapt the notion of arbitrage to this more complex situation and consider stock price dynamics which exclude arbitrage opportunities. Due to volatility uncertainty the market is not complete any more. We establish the interval of no–arbitrage prices for general European contingent claims and deduce explicit results in a Markovian setting.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-441.pdf
    File Function: First version, 2010
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 441.

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    Length: 40 pages
    Date of creation: Nov 2010
    Date of revision:
    Handle: RePEc:bie:wpaper:441

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    Related research

    Keywords: Pricing of contingent claims; incomplete markets; volatility uncertainty; G–Brownian motion stochastic calculus;

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    Cited by:
    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.

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