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

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.