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On the existence of equivalent [tau]-measures in finite discrete time

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  • Schürger, Klaus

Abstract

Suppose that (X(n)) is a finite adapted sequence of d-dimensional random variables defined on some filtered probability space ([Omega], F, (Fn), P). We obtain conditions which are necessary and sufficient for the existence of a probability measure Q equivalent to P (which we call an equivalent [tau]-measure) such that each of the d component sequences of (X(n)) has a prescribed martingale property w.r.t. Q (i.e., it is either a Q-martingale, a Q-sub- or a Q-supermartingale). This extends a version of the Fundamental Theorem of Asset Pricing due to Dalang et al. (1990).

Suggested Citation

  • Schürger, Klaus, 1996. "On the existence of equivalent [tau]-measures in finite discrete time," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 109-128, January.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:1:p:109-128
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    1. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
    3. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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