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Convex hedging of non-superreplicable claims in discrete-time market models

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  • Tomasz Tkalinski

Abstract

All of the papers written so far deal with efficient hedging of contingent claims for which superhedging exists. The goal of this paper is to investigate the convex hedging of contingent claims for which superhedging does not exist. Without superhedging assumption it is still possible to prove the existence of a solution, but one cannot obtain structure of the solution using techniques known so far. Therefore, we develop a new approximative approach to deduce structure of the solution in case of non-superreplicable claims. Copyright The Author(s) 2014

Suggested Citation

  • Tomasz Tkalinski, 2014. "Convex hedging of non-superreplicable claims in discrete-time market models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 239-252, April.
    • Handle: RePEc:spr:mathme:v:79:y:2014:i:2:p:239-252
    DOI: 10.1007/s00186-014-0461-1
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    References listed on IDEAS

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    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    2. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    3. Birgit Rudloff, 2009. "Coherent hedging in incomplete markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 197-206.
    4. Birgit Rudloff, 2007. "Convex Hedging in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 437-452.
    5. Lukasz Stettner, 2000. "Option Pricing in Discrete‐Time Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 305-321, April.
    6. Yumiharu Nakano, 2003. "Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 163-181.
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