Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach

We consider the determination of portfolio processes yielding the highest worst-case bound for the expected utility from final wealth if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. A particular application of our setting is to model crash scenarios where both the number and the height of the crash are uncertain but bounded. Also the situation of changing market coefficients after a possible crash is analyzed.     

A hybrid formulation of eddy current problems

In this article we examine the well‐known magneto‐quasistatic eddy current model for the behavior of low‐frequency electromagnetic fields. We restrict ourselves to formulations in the frequency domain and linear materials, but admit rather general topological arrangements. The generic eddy current model allows two dual formulations, which may be dubbed E‐based and H‐based. We investigate the so‐called hybrid approach that combines both formulations by means of coupling conditions across the boundaries of conducting regions. The resulting continuous and discrete variational formulations will be discussed, and an optimal error estimate for edge finite elements will be proved. It is worthy to note that for this approach no difficulties arise from the topology of the conducting regions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Peptide synthesis by means of immobilized enzymes

-Chymotrypsin covalently bound to silica, enzacryl AA, and enzacryl AH catalyzes peptide bond formation between N-protected dipeptide methyl esters and H-Leu-NH₂ with results similar to those with the free enzyme. The influence of water-miscible and water-immiscible cosolvents, of the supports, and of the structure of the substrates is shown to be of importance for the ease of the chymotrypsin-medicated coupling reactions. The best yields were obtained using biphasic aqueous-organic solvent mixtures, silica-bound chymotrypsin, and substrates with leucine in the P₂-position. The yields of the syntheses are discussed in terms of the reactivity of substrates with similar structure in enzymatic hydrolyses. All the immobilized chymotrypsin preparations could be re-utilized successfully for further couplings. Abbreviations: IUPAC/IUB rules for peptides are followed, see Eur. J. Biochem.27, 201 (1972); Glt=4-carboxybutyrul (glutaryl),-Nan=4-nitroanilide. All amino acids except glycine are of L-configuration.