Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European,One-Touch,lookback or forward starting options

We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability $1?\epsilon$ where $\epsilon$ can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.¹     

Alkylation of Unsaturated Aldehyde and Allylic Bisacetate With Organomanganese Reagents in Presence of Tetrakis Acetonitrile Copper(I) Tetrafluroborate

The conjugate addition of organomanganese reagents to α,β‐unsaturated aldehydes and allylic bisacetate in presence of Me₃Si‐Cl and tetrakis acetonitrile copper(I) tetrafluroborate is described.     

Organocatalytic Conjugate Addition of Azide Ion to α,β‐Unsaturated Aldehydes

An efficient and simple amine‐catatalyzed azide conjugate addition to α,β‐unsaturated aldehydes has been developed. In the presence of a catalytic amount of tertiary amine with a 1:1 mixture of NaN₃ and 37% HCl in CH₂Cl₂, α,β‐unsaturated aldehydes provided β‐azido aldehydes, which could be transformed into 1,3‐amino alcohols.     

The contribution of K.-H. Elster to generalized conjugation theory and nonconvex duality

This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization.     

Mediated Generation of Conjugate Acid by UV and Blue Sensitizers with Upconversion Nanoparticles at 980 nm

NIR and UV exposure of systems comprising upconversion nanoparticles ( UCNP ) based on NaYF₄:Tm/Yb@NaYF₄, a sensitizer absorbing either in the blue or UV region, and an onium salt with weak coordinating anion resulted in formation of conjugate acid (con-H⁺). That was namely Ivocerin (di(4-methoxybenzoyl)diethylgermane), ITX (2-iso-propyl thioxanthone), anthracene, pyrene, rubrene, camphore quinone, and a strong fluorescent coumarin (1,1,6,6,8-pentamethyl-2,3,5,6-tetrahyhdro-1H,4H-11-oxa-3a-aza-benzo[de]anthracene-10-one). Quantification occurred by treatment with Rhodamine B lactone whose color switched to intensive red after photolytic formation of con-H⁺. Exposure with a NIR laser at 980 nm resulted in less con-H⁺ compared to 395 nm where all sensitizers absorb radiation. UCNP did not mainly interfered formation of con-H⁺. The different rates obtained in both experiments responsibly explain the failure and success to initiate polymerization of epoxides applying ether 980 nm or 395 nm excitation, respectively.     

Enantioselective Synthesis of Boron‐Substituted Quaternary Carbon Stereogenic Centers through NHC‐Catalyzed Conjugate Additions of (Pinacolato)boron Units to Enones

The first examples of Lewis base catalyzed enantioselective boryl conjugate additions (BCAs) that generate products containing boron‐substituted quaternary carbon stereogenic centers are disclosed. Reactions are performed in the presence of 1.0–5.0 mol % of a readily accessible chiral accessible N‐heterocyclic carbene (NHC) and commercially available bis(pinacolato)diboron; cyclic or linear α,β‐unsaturated ketones can be used and rigorous exclusion of air or moisture is not necessary. The desired products are obtained in 63–95 % yield and 91:9 to >99:1 enantiomeric ratio (e.r.). The special utility of the NHC‐catalyzed approach is demonstrated in the context of an enantioselective synthesis of natural product antifungal (?)‐crassinervic acid.     

A novel polyaddition of bifunctional acetylenes containing electron-withdrawing groups. III. Synthesis of polymers having β-alkoxyenoate moieties by the reaction of internal diynes with diols

Tri-n-butylphosphine-catalyzed polyadditions of activated internal diynes (bifunctional β-substituted propiolate, 1B and 1C ) with diols are described. Although a terminal bispropiolate ( 1A ) could not produce soluble polymers, with secondary diols, the polyaddition of 1B or 1C with primary as well as secondary diols gave corresponding polymers ( 3 , only composed of E isomeric units) in high yield. The rate of the present polyaddition was estimated by a model reaction of benzyl alcohol with methyl 2-heptynoate ( 4 ), from which the introduction of alkyl groups at the β-position of propiolate moieties was found to decrease the rate of the reaction by 80 times. Furthermore, the rate-determining step on this polymerization system was speculated to be a protonation step of zwitterionic intermediates with protons from diols. © 1996 John Wiley & Sons, Inc.     

Photochemical synthesis: Using light to build C–C bonds under mild conditions

A review of recent advancements in metal-free arylations via photogenerated triplet aryl cations and decatungstate anion ([W₁₀O₃₂]⁴⁻) photocatalyzed C–C bond formation is reported herein. These approaches are two examples of the great potentialities of photons as green activants in organic synthesis, allowing the functionalization of different chemical substrates under mild conditions (room temperature, aqueous solvents, absence of aggressive and unstable reactants and of expensive transition metal-based catalysts, and chance to use solar light as the energy source).     

Batalin–Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras

We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras. We first establish a Van den Bergh duality at the level of complex. Then based on the results of Solotar et al., we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras, and translate the homological information into cohomological one by virtue of the Van den Bergh duality, obtaining the desired Batalin–Vilkovisky algebra structures. Finally, we apply our results to quantum weighted projective lines and Podleś quantum spheres, and the Batalin–Vilkovisky algebra structures for them are described completely.