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Hedging under multiple risk constraints

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  • Ying Jiao
  • Olivier Klopfenstein
  • Peter Tankov

Abstract

Motivated by the asset-liability management of a nuclear power plant operator, we consider the problem of finding the least expensive portfolio, which outperforms a given set of stochastic benchmarks. For a specified loss function, the expected shortfall with respect to each of the benchmarks weighted by this loss function must remain bounded by a given threshold. We consider different alternative formulations of this problem in a complete market setting, establish the relationship between these formulations, present a general resolution methodology via dynamic programming in a non-Markovian context and give explicit solutions in special cases.

Suggested Citation

  • Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2013. "Hedging under multiple risk constraints," Papers 1309.5094, arXiv.org.
    • Handle: RePEc:arx:papers:1309.5094
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    References listed on IDEAS

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    1. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    2. Gundel, Anne & Weber, Stefan, 2007. "Robust utility maximization with limited downside risk in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1663-1688, November.
    3. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    4. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    5. Jules H. van Binsbergen & Michael W. Brandt, 2007. "Optimal Asset Allocation in Asset Liability Management," NBER Working Papers 12970, National Bureau of Economic Research, Inc.
    6. Bruno Bouchard & Thanh Nam Vu, 2012. "A Stochastic Target Approach for P&L Matching Problems," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 526-558, August.
    7. Martellini, Lionel & Milhau, Vincent, 2012. "Dynamic allocation decisions in the presence of funding ratio constraints," Journal of Pension Economics and Finance, Cambridge University Press, vol. 11(4), pages 549-580, October.
    8. Detemple, Jérôme & Rindisbacher, Marcel, 2008. "Dynamic asset liability management with tolerance for limited shortfalls," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 281-294, December.
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    Cited by:

    1. Bruno Bouchard & Jean-François Chassagneux & Géraldine Bouveret, 2016. "A backward dual representation for the quantile hedging of Bermudan options," Post-Print hal-01069270, HAL.

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