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Good deal bounds induced by shortfall risk

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  • Takuji Arai
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    Abstract

    We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on Orlicz hearts. In addition, we obtain its representation with the minimal penalty function. Moreover, we give a representation, for two simple cases, of good deal bounds and calculate the optimal strategies when a claim is traded at the upper or lower bounds of its good deal pricing bound.

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    File URL: http://arxiv.org/pdf/0802.4141
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0802.4141.

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    Date of creation: Feb 2008
    Date of revision: Mar 2010
    Handle: RePEc:arx:papers:0802.4141

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    Web page: http://arxiv.org/

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    1. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    2. Stefan Jaschke & Uwe K├╝chler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    3. repec:wop:humbsf:1997-31 is not listed on IDEAS
    4. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161.
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