Formal total syntheses of the naturally occurring deaminated sialic acids KDN (2), a potential oncofetal antigen, and N-acetylneuraminic acid (Neu5Ac, 1), the most naturally abundant sialic acid, have been accomplished in 46% and 9.3% overall yield, respectively, via a novel ketalization/ring-closing metathesis sequence. The rapid introduction of all oxygen and nitrogen functionality in a completely stereocontrolled manner exploited a rigid 6,8-dioxabicyclo[3.2.1]oct-2-ene template. The 2,7-anhydro-KDN derivative 40 served as an advanced intermediate in each of the two syntheses.

The direct approach: The efficient use of substrate control has served as the basis for the enantioselective total synthesis of (R,R,R)‐α‐tocopherol. A single reagent directing group (ortho‐diphenylphosphanyl benzoate, o‐DPPB) served to control the stereoselectivity of a rhodium‐catalyzed hydroformylation reaction and the directed allylic substitution as the fragment‐coupling step (see picture).

Der direkte Weg: Eine effiziente Substratkontrolle wurde in der enantioselektiven Totalsynthese von (R,R,R)‐α‐Tocopherol genutzt. Hierbei steuert eine einzige ortho‐Diphenylphosphanylbenzoat‐Gruppe (o‐DPPB) die Stereoselektivität der rhodiumkatalysierten Hydroformylierung und der allylischen Substitution im Fragmentkupplungsschritt (siehe Strukturformel).

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The notion of statistical arbitrage introduced in Bondarenko (2003) is generalized to statistical-arbitrage corresponding to trading strategies which yield positive gains on average in a class of scenarios described by a-algebra. This notion contains classical arbitrage as a special case. Admitting general static payoffs as generalized strategies, as done in Kassberger and Liebmann (2017) in the case of one pricing measure, leads to the notion of generalized statistical-arbitrage. We show that even under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we prove that the characterization in Bondarenko (2003), no statistical arbitrage being equivalent to the existence of an equivalent local martingale measure with a path-independent density, is not correct in general. We establish that this equivalence holds true in complete markets and we derive a general sufficient condition for statistical-arbitrages. As a main result we derive the equivalence of no statistical-arbitrage to no generalized statistical-arbitrage. In the second part of the paper we construct several classes of profitable generalized strategies with respect to various choices of the-algebra. In particular, we consider several forms This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.