Abstract
An integral type representation and various extension theorems for monotone linear operators in L p -spaces are considered in relation to market price modelling. As application, a characterization of the existence of a risk-neutral probability measure equivalent to the applied underlying one is provided in terms of the given prices. These results are in the line of the fundamental theorem of asset pricing. Here, in particular, the risk-neutral probability measure considered has the advantage of having its density laying in pre-considered upper and lower bounds.
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Albeverio, S., Di Nunno, G. & Rozanov, Y.A. Price Operators Analysis in L p -Spaces. Acta Appl Math 89, 85–108 (2005). https://doi.org/10.1007/s10440-005-9007-0
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DOI: https://doi.org/10.1007/s10440-005-9007-0