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Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints


  • Yumiharu Nakano


The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete-time financial models with cone-constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super-hedging a contingent claim, which is represented as a Neyman-Pearson-type random variable.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:163-181
    DOI: 10.1080/1350486032000102924

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    Cited by:

    1. A. Jobert & L. C. G. Rogers, 2008. "Valuations And Dynamic Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 1-22.
    2. repec:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9899-y is not listed on IDEAS
    3. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    4. Martin Glanzer & Georg Ch. Pflug & Alois Pichler, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709,, revised Jun 2018.
    5. 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.
    6. Nakano, Yumiharu, 2004. "Minimization of shortfall risk in a jump-diffusion model," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 87-95, March.
    7. Birgit Rudloff, 2016. "Convex Hedging in Incomplete Markets," Papers 1604.08070,
    8. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.


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