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CAS: Computing Semiparametric Bounds on the Expected Payments of Insurance Instruments via Column Generation

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Figure

Figure 1.  Expected LER bounds (left) and gaps (right) for different values of the deductible d, when   the mean l = 50, and variance r 2  = 225 of the underlying loss, as well as its potential maximum value
Figure 2 also highlights the result discussed in  Theorem 3. The bound computed using uniform  mix-ture components is greater than the unimodal bound  from the lognormal mixture with the gap size under  4%
Figure 4.  PDFs and CDFs that yield the optimal bounds via lognormal mixtures (cf. Algorithm 2)   for ` = {11.34, 13.75}, compared with an associated lognormal distribution.
Figure 5.  Illustration of how the upper bound  with mixture components (10) converges to  the unimodality bound (6) (without smoothness  requirements) as g ã Ç
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