Martingale Measures For A Class of Right-Continuous Processes
AbstractThe subject of the present paper is the following. Suppose that "W" is a class of adapted, right-continuous processes on the continuous time horizon [0, 1], and for every stopping time and "W", () is bounded below. A necessary and sufficient condition will be given for the existence of a probability measure "Q" which is equivalent to the original measure and such that each process in "W" is a martingale under "Q". If the processes in "W" represent the discounted prices of available securities, then the condition given here for the existence of a martingale measure can be interpreted as absence of "free lunch" in the securities market. This is a familiar kind of theorem from the finance literature; the novelty of this paper is that the security prices are not required to be in "LP" for some 1 "p", nor are they assumed to be continuous. Also, the concept of free lunch is invariant under the substitution of the original probability measure by an equivalent probability measure. the assumption that () is bounded below for every "W" and stopping time is quite natural since prices are nonnegative. Copyright 1993 Blackwell Publishers.
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Volume (Year): 3 (1993)
Issue (Month): 1 ()
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