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Dynamic Minimization of Worst Conditional Expectation of Shortfall

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  • Jun Sekine

Abstract

In a complete financial market model, the shortfall‐risk minimization problem at the terminal date is treated for the seller of a derivative security F. The worst conditional expectation of the shortfall is adopted as the measure of this risk, ensuring that the minimized risk satisfies certain desirable properties as the dynamic measure of risk, as proposed by Cvitanić and Karatzas (1999). The terminal value of the optimized portfolio is a binary functional dependent on F and the Radon‐Nikodym density of the equivalent local martingale measure. In particular, it is observed that there exists a positive number x* that is less than the replicating cost xF of F, and that the strategy minimizing the expectation of the shortfall is optimal if the hedger's capital is in the range [x*, xF].

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  • Jun Sekine, 2004. "Dynamic Minimization of Worst Conditional Expectation of Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 605-618, October.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:4:p:605-618
    DOI: 10.1111/j.0960-1627.2004.00207.x
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    Cited by:

    1. Paul Embrechts & Alexander Schied & Ruodu Wang, 2018. "Robustness in the Optimization of Risk Measures," Papers 1809.09268, arXiv.org, revised Feb 2021.
    2. Li, Jing & Xu, Mingxin, 2009. "Minimizing Conditional Value-at-Risk under Constraint on Expected Value," MPRA Paper 26342, University Library of Munich, Germany, revised 25 Oct 2010.
    3. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    4. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    5. Pascal François & Geneviève Gauthier & Frédéric Godin, 2012. "Optimal Hedging when the Underlying Asset Follows a Regime-switching Markov Process," Cahiers de recherche 1234, CIRPEE.
    6. Alexander Cherny, 2007. "Pricing and hedging European options with discrete-time coherent risk," Finance and Stochastics, Springer, vol. 11(4), pages 537-569, October.
    7. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, vol. 1(3), pages 1-29, November.

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