Beyond Black-Scholes: semimartingales and Lévy processes for option pricing

We consider the problem of option pricing when the underlying asset follows a general semimartingale process. After reviewing the foundations of arbitrage pricing theory for semimartingales and the link with Lévy processes, we introduce a general method to price options in this framework based on Fourier and Wavelet analysis. Received 4 September 2000     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

Proton-neutron interaction at N≅Z — First observation of the Tz=1 nucleus 46 94 Pd48 in-beam

The neutron deficient nucleus⁹⁴Pd was identified and studied for the first time by in-beam spectroscopy. An I=(14⁺) isomer with t_1/2=0.8 (2) s was observed in a recoil catcher setup inside the multi-detector -array OSIRIS. Filter detectors for neutrons and charged particles were used to identify the (2p2n) exit channel of the reaction⁵⁸Ni+⁴⁰Ca, populated with only 0.06% of the total evaporation residue cross section. The structure of the isomer is discussed within the frame work of shell model calculations in the (p_1/2,g_9/2) model space with emphasis on the g ₉ ^2/2 T=0, I=1,9 pairing two-body matrix elements.Communicated by: D. Schwalm     

Coulomb corrections to Delbrück scattering

The emission of high-energy-rays in the deexcitation of hot⁴⁰Ca and³⁹K nuclei formed in heavy-ion fusion reactions at excitation energyE _x 90 MeV has been studied. The high energy-rays were measured in coincidence with evaporation residues or light charged particles. The spectrum from the self-conjugated compound nucleus⁴⁰Ca shows an appreciable yield suppression in the Giant Dipole Resonance (GDR) energy region with respect to the³⁹K, due to isospin selection rules in the dipole-decay. The spectral line shapes of the spectra are well reproduced by using a statistical code which treats explicitly the isospin quantum number in evaluating level densities and transmission coefficients. The GDR parameters determined from the present coincidence measurements are in good agreement with the systematic in theA 40 mass region at lower bombarding energy based on the analysis of inclusive spectra.We thank M. Caldogno for technical support in the development of evaporation residues detectors. We acknowledge the participation of M. Anghinolfi, P. Corvisiero, M. Taiuti and A. Zucchiatti in the early stages of this work. Thanks are due to M. Kicinska-Habior for providing the isospin-dependent code. Discussions with B. Fornal are also gratefully acknowledged.     

Intermittency in the Fisher's droplet model

Intermittent behaviour of fragment multiplicity distributions in the nuclear liquid-gas phase transition is studied in terms of the droplet model of Fisher. The anomalous fractal dimensions are compared with data on heavy ion reactions and classical molecular dynamics simulations. A signature of the transition in the anomalous fractal dimensions is shown.We thank Profs. S. Ayik, M. Di Toro and V. Kondratyev for discussions. One of us (T.K.) acknowledges the support of INFN-LNS.     

Precision measurement of theg-factor of the 2+ γ-vibrational state of160Dy and test of theF-spin purity

The rotations of the 392-966 keV and the 299–966 keV directional correlations of¹⁶⁰Dy in the static hyperfine field of DyTb have been measured with high precision. A neutron activated Tb single crystal was used which was magnetized to saturation at 4.2 K by an external magnetic field of 4.5 T applied in the direction of theb-axis. The agreement of both rotations proves that the relaxation of the 4f-shell after the-decay takes less than 10 ps. A quantum mechanical calculation within the magnon model gave a relaxation time of the order of 1 ps. Theg-factor of the 2⁺ -vibrational state was derived as

Equivalent formulations of ＂the equation of life＂

Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named "the equation of life". Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerful Boltzmann–Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology.     

Laser Chemical Processing (LCP)—A versatile tool for microstructuring applications

Laser Chemical Processing (LCP) is presented as a novel microstructuring method for multiple applications. Via the combination of a chemical liquid jet and a laser beam, thermochemical and photochemical reactions can be initiated. Due to the free choice of the chemistry for the carrier liquid and the laser source, efficient processes can be devised for a large variety of applications. We present some examples for the microstructuring of silicon with the focus on etching, selective doping of phosphorous and the combination of etching and doping.     

Deposition and stoichiometry control of Nd-doped gadolinium gallium garnet thin films by combinatorial pulsed laser deposition using two targets of Nd:Gd<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> and Ga<Subscript>2</Subscript>O<Subscript>3</Subscript>

We have demonstrated pulsed laser deposition of Nd-doped gadolinium gallium garnet on Y₃Al₅O₁₂ by the simultaneous ablation of two separate targets of Nd:Gd₃Ga₅O₁₂ (GGG) and Ga₂O₃. Such an approach is of interest as a method of achieving stoichiometry control over films whilst the growth parameters are kept constant and optimal for high quality crystal growth. We show here how the stoichiometry and resultant lattice parameter of a film can be controlled by changing the relative deposition rates from the two targets. Films have been grown with enough extra Ga to compensate for the deficiency that commonly occurs when depositing only from a GGG target. We have also grown crystalline GGG films with an enriched Ga concentration, and this unconventional approach to film stoichiometry control may have potential applications in the fabrication of films with advanced compositionally graded structures.