Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Polymérisation anionique amorcée par les composés lamellaires du graphite et du lithium

In the present work, we use the binary insertion compound LiC₁₂ to polymerize styrene, methyl methacrylate, butadiene, isoprene, and to copolymerize isoprene and styrene in various hydrocarbon solvents (aromatics and aliphatic) and etheral solvents. We show that the styrene polymerization in aromatic solvents gives better yields than in the etheral solvents, the polymer being atactic. Methyl methacrylate does not polymerize in toluene but does so completely in DME. More generally, the yields of polymerization are better with KC₃₇ than with LiC₁₂ because of the different capacities of the monomer to get into the carbon layers. The polymerization of dienes with LiC₁₂ shows that the microstructures of the polymer obtained in π-or n-donor solvents are similar to the ones obtained by homogenous polymerization with Li cation in such solvents. However, for isoprene in cyclohexane, the results are different. The isoprene styrene copolymers are statistical ones and the mean length of styrene blocks is less than 5. The monomer interaction with the insertion compound and the growing chain geometry between the carbon layers are the facts which control either the stereospecificity of the polymerization or the selectivity of the copolymerization.     

Theoretical and experimental reevaluation of the basicity of lambda3-phosphinine

We have investigated the basicity of phosphinine (C5H5P, phosphabenzene) in reevaluating its proton affinity (PA) and gas-phase basicity (GB) and the pK(a) value of its protonated form. As a necessary step, we have first determined its gas-phase proton affinity. Using both mass spectrometric and quantum chemical methods, we have obtained the values PA(C5H5P) = 195.8 +/- 1.0 kcal mol(-1) and GB(298)(C5H5P) = 188.1 +/- 1.0 kcal mol(-1), in good agreement with previous results. We then derived a value of pK(a)(C5H6P+) = -16.1 +/- 1.0 in aqueous solution using three different approaches: the latter markedly differs from the currently available value of -10. The reason for such a discrepancy in the pK(a) of protonated phosphinine in solution is discussed. In the theoretical determination of PAs, evaluation of the basis set superposition error (BSSE) showed that this effect is quite small, being 0.1-0.2 kcal mol(-1) for phosphinine, when a density functional theory (DFT) method in conjunction with a large basis set were used.     

Phenomenes de complexation entre un peroxyde et les monomeres vinyliques polaires etudies par resonance magnetique protonique

The self association of cumyl hydroperoxide and its complexing with polar monomers have been studied by proton magnetic resonance. These complexations are exothermic and strongly temperature dependent. It has been suggested that the complexation of cumyl hydroperoxide by polar monomers could be one of the causes of its efficiency in initiating the radical polymerization of vinyl monomers on an ethyl-zinc terminated polyethylene chain to form radical block copolymers. However, if this phenomenon has an effect on the initiation, it should not affect the propagation mechanisms, because the hydroperoxide is destroyed by ZnEt₂ during initiation. Moreover, the tacticity of radical polymethylmethacrylate, obtained at 60° with (ZnEt₂—cumyl hydroperoxide) in heptane does not differ from the conventional radical polymer.     

Conformations of luteoskyrin and rugulosin in solution

The pigments Luteoskyrin (Ls) and Rugulosin (Rg) might adopt a priori two extreme conformations, a planar and an angular one. To determine the predominant conformation in solution, the nature of the lowest energy transition of the chromophores and the presence of intramolecular H-bonding have been investigated. The solvent effects on electronic absorption and CD spectra indicated the π-π* nature of the lowest energy transition. Treatments of the electronic absorption results according to McRae and Kosower relations, IR absorption and PMR spectra suggested the presence of strong intra-molecular H-bonds. From these results it was concluded that Ls and Rg adopted in a variety of solvents the most planar conformation.     

Investigation of oligomethylmethacrylate-lithium and its donor-acceptor complexes with organometal compounds by means of infrared spectroscopy

Anionic polymerization of methyl methacrylate in THF and toluene at ?70° was studied by means of i.r. spectroscopy. The reaction mixtures show characteristic absorption at 1600–1750 cm^?1 caused by the stretching vibrations of the propagating centre as well as by the groups obtained in side reactions (metal splitting, addition to a carbonyl group, cyclization). Sec-butyllithium is more effective in THF than n-butyllithium, ethyllithium and fluorenyllithium. When polymerizing in toluene, small amounts of a donor (THF or HMPT) cause formation of active centres similar to those in pure THF. The “living” ends of oligo-MMA form 1:1 complexes with electron acceptors such as trialkylaluminium and triethylboron.