The issue of constructing a risk minimizing hedge with additional constraints on the shortfall risk is examined. Several classical risk minimizing problems have been adapted to the new setting and solved.  The existence and specific forms of optimal strategies in a general semimartingale market model with the use of conditional statistical tests have been proven. The  quantile hedging method applied in \mbox{%DIFAUXCMD FL10pt%DIFAUXCMD and \mbox{%DIFAUXCMD FL2 }0pt%DIFAUXCMD } as well as the classical Neyman-Pearson lemma have been generalized. Optimal hedging strategies with shortfall constraints in the Black-Scholes and exponential Poisson model have been explicitly determined.
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 0pt%DIFAUXCMD and \mbox{%DIFAUXCMD FL2 }0pt%DIFAUXCMD } 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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with additional constraints
under an additional almost-surely type constraint
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risk
profile
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have been
are
A
In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minimizing setting is ruled out.
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specific
concrete
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have been
are
A
well known
D
applied in \mbox{%DIFAUXCMD FL1
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have been
are
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have been
are