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On the shortfall risk control -- a refinement of the quantile hedging method

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  • Micha{l} Barski

Abstract

The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minimizing setting is ruled out. The existence and concrete forms of optimal strategies in a general semimartingale market model with the use of conditional statistical tests are proven. The well known quantile hedging method as well as the classical Neyman-Pearson lemma are generalized. Optimal hedging strategies with shortfall constraints in the Black-Scholes and exponential Poisson model are explicitly determined.

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  • Micha{l} Barski, 2014. "On the shortfall risk control -- a refinement of the quantile hedging method," Papers 1402.3725, arXiv.org, revised Dec 2015.
    • Handle: RePEc:arx:papers:1402.3725
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    References listed on IDEAS

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    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    2. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    3. Birgit Rudloff, 2007. "Convex Hedging in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 437-452.
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