Computing semiparametric bounds on the expected payments of insurance instruments via column generation

It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use column generation, a classical optimization technique, to address these limitations. From column generation, it follows that practical univari- ate semiparametric bounds can be found by solving a series of linear programs. In addition to moment information, the column generation approach allows the inclusion of extra information about the random variable; for instance, unimodality and continuity, as well as the construction of corresponding worst/best-case distributions in a simple way

Induction of stimulative parthenocarpy in Vitis vinifera L.

Stimulative parthenocarpy was induced in two varieties of Vitis vinifera L. Flame Tokay and Rose Muscat (local variety) out of eight varieties studied.In F l a m e T o k a y the delay or inhibition of bhe abscission of the calyptra and parthenocarpic development of the berries, was obtained with pre-bloom treatments (3 days before beginning of bloom) of 4CPA 30 ppm + KGA3 30 ppm. Induction and growth ,of parthenocarpic berries was most pronounced after post-bloom sprays (7 days after the end of bloom) with BA 1500 ppm + KGA3 80 ppm or 4CPA 30 ppm. A parthenocarpic development of the berries was also obtained with postbloom treatments of KGA3 at concentrations of 50 to 100 ppm. BA (Benzyladenine) alone had only a slight effect on the development of parthenocarpic berries. However, the results were surprisingly satisfactory when applied in combination with gibberellin (KGA3 80 ppm) or auxins. Treatments at bloom or after bloom with BA 800 ppm + KGA3 80 ppm increased bhe number of berries and cluster weight. Applications of BA 800 ppm + KGA3 80 ppm to Rose Musca t at the beginning of bloom resulted in clusters with practically all berries seedless. The artificially accelerated growth of the berries may provoke abortion of all the recently fecundated ovules and the non viability of the not fecundated ones. Clusters of the treated plants with an average of 520 flowers originated 501 parbhenocarpic berries (96%), whereas the control with an average 635 flowers per cluster gave a percentage of seeded + seedless berries of 14% only {95 berries per cluster). BA applied with auxin or gibberellin-like substances in full-bloom or after bloom produced seedless berries, which were smaller in size than the seeded berries of unsprayed clusters

Copositive certificates of non-negativity for polynomials on semialgebraic sets

A certificate of non-negativity is a way to write a given function so that its non-negativity becomes evident. Certificates of non-negativity are fundamental tools in optimization, and they underlie powerful algorithmic techniques for various types of optimization problems. We propose certificates of non-negativity of polynomials based on copositive polynomials. The certificates we obtain are valid for generic semialgebraic sets and have a fixed small degree, while commonly used sums-of-squares (SOS) certificates are guaranteed to be valid only for compact semialgebraic sets and could have large degree. Optimization over the cone of copositive polynomials is not tractable, but this cone has been well studied. The main benefit of our copositive certificates of non-negativity is their ability to translate results known exclusively for copositive polynomials to more general semialgebraic sets. In particular, we show how to use copositive polynomials to construct structured (e.g., sparse) certificates of non-negativity, even for unstructured semialgebraic sets. Last but not least, copositive certificates can be used to obtain not only hierarchies of tractable lower bounds, but also hierarchies of tractable upper bounds for polynomial optimization problems.Comment: 27 pages, 1 figur