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

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  • Yumiharu Nakano

Abstract

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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    Citations

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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. 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.
    3. Martin Glanzer & Georg Ch. Pflug, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709, arXiv.org, revised Nov 2017.
    4. 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.
    5. Nakano, Yumiharu, 2004. "Minimization of shortfall risk in a jump-diffusion model," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 87-95, March.
    6. Birgit Rudloff, 2016. "Convex Hedging in Incomplete Markets," Papers 1604.08070, arXiv.org.
    7. 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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