Fourier Inversion Formulas in Option Pricing and Insurance

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.      

Loop calculations for the non-commutative U ⋆(1) gauge field model with oscillator term

The European Physical Journal C - Motivated by the success of the non-commutative scalar Grosse–Wulkenhaar model, a non-commutative U ⋆(1) gauge field theory including an...     

Effect of 1-Aminoanthracene (1-AMA) Binding on the Structure of Three Lipocalin Proteins,the Dimeric β Lactoglobulin,the Dimeric Odorant Binding Protein and the Monomeric α<Subscript>1</Subscript>-Acid Glycoprotein. Fluorescence Spectra and Lifetimes Studies

We studied effect of 1-aminoanthracene (1-AMA) binding on the structures of dimeric β lactoglobulin, dimeric odorant binding protein (OBP) and monomeric α₁-acid glycoprotein (lipocalin family proteins) by monitoring fluorescence excitation spectra and measuring fluorescence lifetimes of the tryptophan residues of the proteins. Results show that binding of 1-AMA to β lactoglobulin and OBP modifies their conformation even at low probe concentration compared to that of the proteins. Structural modification induces a red shift of the fluorescence excitation spectra maximum of tryptophan residues accompanied with an increase of the third fluorescence lifetime and a decrease of its pre-exponential factor. These effects were not observed for α₁-acid glycoprotein, probably as the result of carbohydrate presence. These data raise doubts concerning use of 1-AMA as a probe to study biological properties of β lactoglobulin and OBP.     

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.