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Pricing Without Equivalent Martingale Measures Under Complete and Incomplete Observation

In: Contemporary Quantitative Finance

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  • Giorgia Galesso

    (University of Padova, Department of Pure and Applied Mathematics)

  • Wolfgang J. Runggaldier

    (University of Padova, Department of Pure and Applied Mathematics)

Abstract

Traditional arbitrage pricing theory is based on martingale measures. Recent studies show that there are situations when there does not exist an equivalent martingale measure and so the question arises: what can one do with pricing and hedging in this situation? We mention here two approaches to this effect that have appeared in the literature, namely the “Fernholz-Karatzas” approach and Platen’s “Benchmark approach” and discuss their relationships both in models where all relevant quantities are fully observable as well as in models where this is not the case and, furthermore, not all observables are also investment instruments.

Suggested Citation

  • Giorgia Galesso & Wolfgang J. Runggaldier, 2010. "Pricing Without Equivalent Martingale Measures Under Complete and Incomplete Observation," Springer Books, in: Carl Chiarella & Alexander Novikov (ed.), Contemporary Quantitative Finance, pages 99-121, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03479-4_6
    DOI: 10.1007/978-3-642-03479-4_6
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