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Coherent price systems and uncertainty-neutral valuation

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  • Patrick Beißner

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    (Center for Mathematical Economics, Bielefeld University)

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    Abstract

    We consider fundamental questions of arbitrage pricing arising when the uncertainty model incorporates volatility uncertainty. The resulting ambiguity motivates a new principle of preference-free valuation. By establishing a microeconomic foundation of sublinear price systems, the principle of ambiguity-neutral valuation imposes the novel concept of equivalent symmetric martingale measures. Such measures exist when the asset price with uncertain volatility is driven by Peng's G-Brownian motion.

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    File URL: http://www.imw.uni-bielefeld.de/n/upload/paper/32bb90e8976aab5298d5da10fe66f21d.pdf
    File Function: Second version, 2013
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 464.

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    Length: 41 pages
    Date of creation: Nov 2013
    Date of revision:
    Handle: RePEc:bie:wpaper:464

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    Related research

    Keywords: mutually singular priors; uncertain volatility; sublinear expectation; viability of sublinear price systems; arbitrage; equivalent symmetric martingale measures set (EsMM set); symmetric martingales; Girsanov for G-Brownian motion;

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    1. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    2. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
    3. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    4. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
    5. repec:fth:inseep:9513 is not listed on IDEAS
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