LOWER AND UPPER BOUNDS OF MARTINGALE MEASURE DENSITIES IN CONTINUOUS TIME MARKETS

In a continuous time market model we consider the problem of existence of an equivalent martingale measure with density lying within given lower and upper bounds and we characterize a necessary and sufficient condition for this. In this sense our main result can be regarded as a version of the fundamental theorem of asset pricing. In our approach we suggest an axiomatic description of prices on L_p ‐spaces (with p ∈[1, ∞)) and we rely on extension theorems for operators.