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On hedging in finite security markets

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  • Silvia Florio
  • Wolfgang Runggaldier

Abstract

A market is considered where trading can take place only at discrete time points, the trading frequency cannot grow without bound, and the number of states of nature is finite. The main objectives of the paper are to show that the market can be completed also with highly correlated risky assets, and to describe an efficient algorithm to compute a self-financing hedging strategy. The algorithm consists off-line of a backwards recursion and on-line of the solution, in each period, of a system of linear equations; it is a consequence of a proof where, using a well-known mathematical property, it is shown that uniqueness of the martingale measure implies completeness also in our setting. The significance of 'multistate' models versus the familiar binomial model is discussed and it is shown how the evolution of prices of the (correlated) risky assets can be chosen so that a given probability measure is already the unique equivalent martingale measure.

Suggested Citation

  • Silvia Florio & Wolfgang Runggaldier, 1999. "On hedging in finite security markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 159-176.
    • Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:159-176
    DOI: 10.1080/135048699334519
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    3. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    4. Ward Whitt, 1978. "Approximations of Dynamic Programs, I," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 231-243, August.
    5. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    7. Girotto, Bruno & Ortu, Fulvio, 1997. "Numeraires, equivalent martingale measures and completeness in finite dimensional securities markets," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 283-294, April.
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