No-arbitrage conditions,scenario trees,and multi-asset financial optimization

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem’s random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset–liability or portfolio management.     

Implicit runge-kutta methods for differential inclusions

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.     

The natural Banach space for version independent risk measures

Risk measures, or coherent measures of risk, are often considered on the space L^∞$L^{\infty }$, and important theorems on risk measures build on that space. Other risk measures, among them the most important risk measure–the Average Value-at-Risk–are well defined on the larger space L¹$L^1$ and this seems to be the natural domain space for this risk measure. Spectral risk measures constitute a further class of risk measures of central importance, and they are often considered on some L^p$L^p$ space. But in many situations this is possibly unnatural, because any L^p$L^p$ with p>_p0$p>p_0$, say, is suitable to define the spectral risk measure as well. In addition to that, risk measures have also been considered on Orlicz and Zygmund spaces. So it remains for discussion and clarification, what the natural domain to consider a risk measure is?     

Alkyne gem‐Hydrogenation: Formation of Pianostool Ruthenium Carbene Complexes and Analysis of Their Chemical Character

Parahydrogen (p‐H₂) induced polarization (PHIP) NMR spectroscopy showed that [Cp^XRu] complexes with greatly different electronic properties invariably engage propargyl alcohol derivatives into gem‐hydrogenation with formation of pianostool ruthenium carbenes; in so doing, less electron rich Cp^X rings lower the barriers, stabilize the resulting complexes and hence provide opportunities for harnessing genuine carbene reactivity. The chemical character of the resulting ruthenium complexes was studied by DFT‐assisted analysis of the chemical shift tensors determined by solid‐state ¹³C NMR spectroscopy. The combined experimental and computational data draw the portrait of a family of ruthenium carbenes that amalgamate purely electrophilic behavior with characteristics more befitting metathesis‐active Grubbs‐type catalysts.     

Total Synthesis of an Exceptional Brominated 4‐Pyrone Derivative of Algal Origin: An Exercise in Gold Catalysis and Alkyne Metathesis

A concise approach to the algal metabolite 1 is described, which also determines the previously unknown stereostructure of this natural product. Compound 1 is distinguished by a rare brominated 4‐pyrone nucleus linked as a ketene–acetal to a polyunsaturated macrocyclic scaffold comprising an extra homoallylic bromide entity. The synthesis of 1 is based on the elaboration and selective functionalization of the linear precursor 23 endowed with no less than six different sites of unsaturation including the highly enolized oxo‐alkanoate function. Key to success was the formation of the 2‐alkoxy‐4‐pyrone ring by a novel gold‐catalyzed transformation which engages only the acetylenic β‐ketoester substructure of 23 but leaves all other π‐bonds untouched. The synthesis was completed by a ring‐closing alkyne metathesis to forge the signature cycloalkyne motif of 1 followed by selective bromination of the ketene–acetal site in the resulting product 27 without touching the skipped diene–yne substructure resident within the macrocyclic tether.     

Total Synthesis of Belizentrin Methyl Ester: Report on a Likely Conquest

The assigned structure of the dinoflagellate‐derived toxin belizentrin was prepared by total synthesis in form of the corresponding methyl ester for stability reasons. The successful route features an unusual solution for the preparation of a recalcitrant ylide on a C‐glycosidic segment; moreover, it involves an asymmetric hetero‐Diels–Alder reaction en route to the tertiary hemiacetal substructure, a Negishi cross‐coupling of two elaborate building blocks, and a macrocyclization based on an intramolecular aminolysis of a spirolactone. A modified Kocienski olefination ultimately allowed the polyol side chain to be attached to the macrocycle although this transformation faced the exceptional base sensitivity of this polyunsaturated target compound.     

Untersuchungen über Perylen und seine Derivate

Ohne Zusammenfassung