Portfolio Insurance under a risk-measure constraint
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.4489.
Date of creation: Feb 2011
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-03-05 (All new papers)
- NEP-IAS-2011-03-05 (Insurance Economics)
- NEP-RMG-2011-03-05 (Risk Management)
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- Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012.
"On the interplay between distortion-, mean value- and Haezendonck-Goovaerts risk measures,"
Open Access publications from Katholieke Universiteit Leuven
urn:hdl:123456789/352122, Katholieke Universiteit Leuven.
- Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 10-18.
- Pézier, Jacques & Scheller, Johanna, 2013. "Best portfolio insurance for long-term investment strategies in realistic conditions," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 263-274.
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