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Incomplete Markets: Convergence of Options Values under the Minimal Martingale Measure. The Multidimensional Case

Author

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  • Prigent, J.L.
Abstract
In the setting of incomplete markets, this paper presents a general result of weak convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Follmer and Schweizer is a convenient tool for the stabilization under convergence. This extends previous well-known results when the markets are complete both in discrete time and continuous time. The result is extended to markets with several risky assets and generalizes a previous work on this subject.

Suggested Citation

  • Prigent, J.L., 1997. "Incomplete Markets: Convergence of Options Values under the Minimal Martingale Measure. The Multidimensional Case," Papers 9735, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    • Handle: RePEc:fth:pnegmi:9735
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    Cited by:

    1. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    2. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    3. Hentati-Kaffel, R. & Prigent, J.-L., 2016. "Optimal positioning in financial derivatives under mixture distributions," Economic Modelling, Elsevier, vol. 52(PA), pages 115-124.
    4. Colino, Jesús P., 2008. "Weak convergence in credit risk," DES - Working Papers. Statistics and Econometrics. WS ws085518, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    PRICES ; INTEREST RATE ; ECONOMETRICS ; CONVERGENCE;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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