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Portfolio Insurance under a risk-measure constraint

  • Carmine De Franco
  • Peter Tankov

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor's utility function subject to the risk measure constraint.We give a full solution to this nonconvex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).

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File URL: http://arxiv.org/pdf/1102.4489
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Paper provided by arXiv.org in its series Papers with number 1102.4489.

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Date of creation: Feb 2011
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Handle: RePEc:arx:papers:1102.4489
Contact details of provider: Web page: http://arxiv.org/

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