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Equivalent Locally Martingale Measure for the Deflator Process on Ordered Banach Algebra

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  • Boushra Y. Hussein
  • Antonio Di Crescenzo

Abstract

This paper aims at determining the measure of Q under necessary and sufficient conditions. The measure is an equivalent measure for identifying the given P such that the process with respect to P is the deflator locally martingale. The martingale and locally martingale measures will coincide for the deflator process discrete time. We define s-viable, s-price system, and no locally free lunch in ordered Banach algebra and identify that the s-price system C,π is s-viable if and only a character functional ψC≤π exists. We further demonstrate that no locally free lunch is a necessary and sufficient condition for the equivalent martingale measure Q to exist for the deflator process and the subcharacter ϕ∈Γ such that φC=π. This paper proves the existence of more than one condition and that all conditions are equivalent.

Suggested Citation

  • Boushra Y. Hussein & Antonio Di Crescenzo, 2020. "Equivalent Locally Martingale Measure for the Deflator Process on Ordered Banach Algebra," Journal of Mathematics, Hindawi, vol. 2020, pages 1-7, June.
  • Handle: RePEc:hin:jjmath:5785098
    DOI: 10.1155/2020/5785098
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