Mono- and dinuclear complexes of sulfones with the tetrachlorides of group 4

The reactions of dialkyl sulfones [R(2)SO(2): R = Me, Et, Ph, R(2)=-(CH(2))(4)-] with the metal tetrachlorides of Group 4 [MCl(4): M = Ti, Zr, Hf] give different products mainly depending on the sulfone/M molar ratio. Compounds of formula [M(2)Cl(8)(R(2)SO(2))(2)][M = Ti, R(2)=-(CH(2))(4)-; M = Zr, R = Et, R = Ph] and [MCl(4)(R(2)SO(2))(2)](sulfone/M = 2)[M = Ti, R = Me; M = Zr, R = Me, R = Ph, R(2)=-(CH(2))(4)-; M = Hf, R = Me, R(2)=-(CH(2))(4)-] have been obtained. By X-ray diffraction methods the dinuclear titanium and zirconium adducts, [Ti(2)Cl(8)(mu-sulfolane-O,O')(2)] and [Zr(2)Cl(8)(mu-Ph(2)SO(2)-O,O')(2)] have been established to contain bridging sulfone and hexacoordinated metal centres, while the mononuclear zirconium complex [ZrCl(4)(Me(2)SO(2))(2)] has cis-monodentate sulfones in a slightly distorted octahedral geometry. The reaction between TiCl(4) and sulfolane (tetrahydrothiophene 1,1-dioxide) in SOCl(2) affords the 1:1 adduct independent of the sulfone/Ti molar ratio. Ligand-exchange and inter-conversion between mononuclear and dinuclear species have been observed by NMR, while the spectral features of the SO(2) moiety have been assigned by IR- and Raman spectroscopies.     

Pricing of catastrophe insurance options written on a loss index with reestimation

We propose a valuation model for catastrophe insurance options written on a loss index. This kind of options distinguishes between a loss period [0,T₁], during which the catastrophes may happen, and a development period [T₁,T₂], during which losses entered before T₁ are reestimated. Here we suppose that the underlying loss index is given by a time inhomogeneous compound Poisson process before T₁ and that losses are reestimated by a common factor given by an exponential time inhomogeneous Lévy process after T₁. In this setting, using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options written on this kind of index.     

Dissipative Catalysis with a Molecular Machine

We report on catalysis by a fuel‐induced transient state of a synthetic molecular machine. A [2]rotaxane molecular shuttle containing secondary ammonium/amine and thiourea stations is converted between catalytically inactive and active states by pulses of a chemical fuel (trichloroacetic acid), which is itself decomposed by the machine and/or the presence of additional base. The ON‐state of the rotaxane catalyzes the reduction of a nitrostyrene by transfer hydrogenation. By varying the amount of fuel added, the lifetime of the rotaxane ON‐state can be regulated and temporal control of catalysis achieved. The system can be pulsed with chemical fuel several times in succession, with each pulse activating catalysis for a time period determined by the amount of fuel added. Dissipative catalysis by synthetic molecular machines has implications for the future design of networks that feature communication and signaling between the components.     

Local Risk-Minimization for Defaultable Claims with Recovery Process

We study the local risk-minimization approach for defaultable claims with random recovery at default time, seen as payment streams on the random interval 〚0,τ∧T〛, where T denotes the fixed time-horizon. We find the pseudo-locally risk-minimizing strategy in the case when the agent information takes into account the possibility of a default event (local risk-minimization with G-strategies) and we provide an application in the case of a corporate bond. We also discuss the problem of finding a pseudo-locally risk-minimizing strategy if we suppose the agent obtains her information only by observing the non-defaultable assets.     

Insider trading equilibrium in a market with memory

We consider the Kyle-Back model for insider trading, with the difference that the classical Brownian motion noise of the noise traders is replaced by the noise of a fractional Brownian motion B ^H with Hurst parameter ${H>\frac{1}{2}}$ (when ${H=\frac{1}{2}, B^H}$ coincides with the classical Brownian motion). Heuristically, for ${H>\frac{1}{2}}$ this means that the noise traders has some ??memory??, in the sense that any increment from time t on has a positive correlation with its value at t. (In other words, the noise trading is a persistent stochastic process). It also means that the paths of the noise trading process are more egular than in the classical Brownian motion case. We obtain an equation for the optimal (relative) trading intensity for the insider in this setting, and we show that when ${H\rightarrow\frac{1}{2}}$ the solution converges to the solution in the classical case. Finally, we discuss how the size of the Hurst coefficient H influences the optimal performance and portfolio of the insider.