Equivalent locally martingale measure for the deflator process on ordered Banach algebra (Q780496)

Summary: 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 \((C,\pi)\) is \(s\)-viable if and only a character functional \(\psi|_C\leq\pi\) 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 \(\phi\in\Gamma\) such that \(\varphi|_C=\pi\). This paper proves the existence of more than one condition and that all conditions are equivalent.