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Martingale Measures For A Class of Right-Continuous Processes

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  • Peter Lakner
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    Abstract

    The 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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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 3 (1993)
    Issue (Month): 1 ()
    Pages: 43-53

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    Handle: RePEc:bla:mathfi:v:3:y:1993:i:1:p:43-53

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    Cited by:
    1. A. Fiori Maccioni, 2011. "The risk neutral valuation paradox," Working Paper CRENoS 201112, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    2. Clotilde Napp & Elyès Jouini, 2005. "Arbitrage and state price deflators in a general intertemporal framework," Post-Print halshs-00151526, HAL.
    3. Frittelli, Marco, 1996. "Dominated families of martingale, supermartingale and quasimartingale laws," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 265-277, November.
    4. Jouini, Elyès, 2001. "Arbitrage and control problems in finance: A presentation," Economics Papers from University Paris Dauphine 123456789/5590, Paris Dauphine University.
    5. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245.
    6. Jaime A. Londo\~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274, arXiv.org, revised Feb 2004.
    7. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
    8. Alessandro Fiori Maccioni, 2011. "Endogenous Bubbles in Derivatives Markets: The Risk Neutral Valuation Paradox," Papers 1106.5274, arXiv.org, revised Sep 2011.

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