A general methodology to price and hedge derivatives in incomplete markets

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox-Ross-Rubinstein and Black-Scholes in the complete markets case and the Schweizer and Bouchaud-Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.Comment: 24 pages, LaTeX, epsfig.sty, 5 eps figures, changes in the presentation of the method, submitted to International J. of Theoretical and Applied Financ

A percolation system with extremely long range connections and node dilution

We study the very long-range bond-percolation problem on a linear chain with both sites and bonds dilution. Very long range means that the probability $p_{ij}$ for a connection between two occupied sites $i,j$ at a distance $r_{ij}$ decays as a power law, i.e. $p_{ij} = \rho/[r_{ij}^\alpha N^{1-\alpha}]$ when $0 \le \alpha < 1$, and $p_{ij} = \rho/[r_{ij} \ln(N)]$ when $\alpha = 1$. Site dilution means that the occupancy probability of a site is $0 < p_s \le 1$. The behavior of this model results from the competition between long-range connectivity, which enhances the percolation, and site dilution, which weakens percolation. The case $\alpha=0$ with $p_s =1$ is well-known, being the exactly solvable mean-field model. The percolation order parameter $P_\infty$ is investigated numerically for different values of $\alpha$, $p_s$ and $\rho$. We show that in the ranges $0 \le \alpha \le 1$ and $0 < p_s \le 1$ the percolation order parameter $P_\infty$ depends only on the average connectivity $\gamma$ of sites, which can be explicitly computed in terms of the three parameters $\alpha$, $p_s$ and $\rho$

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

2d frustrated Ising model with four phases

In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely, the vertical bonds are supposed to be non random while the horizontal bonds alternate: one row of all non random horizontal bonds is followed by one row where they are independent dichotomic random variables. We solve the model using an approximate approach that replace the quenched average with an annealed average under the constraint that the number of frustrated plaquettes is keep fixed and equals that of the true system. The surprising fact is that for some choices of the parameters of the model there are three second order phase transitions separating four different phases: antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.Comment: 17 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to Physical Review

Influence of Ageing Time and Method on Beef Quality and Safety

The effectiveness of dry ageing with regard to retaining meat quality is still subject to debate. At 4 d post mortem, samples of boneless strip loins were excised from young Charolais carcasses and then stored for a further 26 d in a cooler, either vacuum-packaged (VP) or dried-aged (DA). Loin samples were also dissected 7 d post mortem as a control treatment (CT). Chemical, instrumental and microbiological data (n = 18) were determined in longissimus dorsi and underwent ANOVA to estimate the differences in the ageing fixed factor split into two orthogonal contrasts: control vs. aged and VP vs. DA. Ageing loss (both surface dehydration and water purge) was greater in DA compared to VP samples, resulting in the lowest moisture content and highest crude protein and fat percentage in DA loins. The ageing method did not affect meat surface colour, except for redness, which had the lowest value in DA samples. Meat tenderness improved a similar amount following both VP and DA ageing treatments. Compared to the control, prolonged ageing raised both the peroxide value and the total microbial count, especially in DA samples, though both remained within the recommended limits. In summation, both ageing methods improved beef meat tenderisation, preserving its shelf life

Quaternary capable folds and seismic hazard in Lombardia (Northern Italy): the Castenedolo structure near Brescia.

We identify evidence of late Quaternary compressive tectonics in the Northern sector of the Central Po Plain through a systematic revision of the literature, new field mapping, and a new study of seismic reflection data obtained by ENI E&P. In particular, the reinterpretation of ca. 18.000 km of seismic profiles clearly shows a belt of segmented, 10 to 20 km long, fault propagation folds, controlled by the Plio-Quaternary growth of several out-of-sequence thrusts. As an example of this active structural style, in this paper we focus on a buried fold located just south of the Castenedolo Hill, a few km SE of Brescia. Although the Castenedolo anticline has long ago been described as a young compressional structure (e.g., DESIO, 1965), no detailed structural analysis of this feature has been performed until now. We calculated the uplift rates of this fold through the analysis of its syntectonic sedimentary record as imaged by the extremely high quality ENI E&P subsurface data available in the area. The evolution of this anticline was a discontinuous process characterized by several tectonic uplift pulses (with rates of ca. 0.1 mm/yr) of different duration, separated by periods of variable extent in which no fold growth occurred. The Quaternary growth history of this anticline and the presence of faulted and folded late Pleistocene to Holocene deposits at nearby sites (Ciliverghe and Monte Netto) demonstrate that the significant seismicity of this area (e.g., the December 25, 1222, Io = IX MCS Brescia earthquake, MAGRI & MOLIN, 1986; GUIDOBONI, 1986) must be related to active compressional structures within the Brescia piedmont belt. Our regional investigations show that the structural and paleoseismic setting illustrated near Castenedolo is typical of the whole Lombardia domain of the Southern Alps. This implies that the currently accepted seismotectonic model for this region, and related seismic hazard assessment, should be thoroughly and carefully re-evaluated

Statistical properties of genealogical trees

We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution, we measure the distribution of ancestors appearing more than once in a given tree. After a transient time, the probability of repetition follows, up to a rescaling, a stationary distribution which we calculate both numerically and analytically. This distribution exhibits a universal shape with a non-trivial power law which can be understood by an exact, though simple, renormalization calculation. Some real data on human genealogy illustrate the problem, which is relevant to the study of the real degree of diversity in closed interbreeding communities.Comment: Accepted for publication in Phys. Rev. Let

Prospective Analysis of STRATAFIX™ Symmetric PDS Plus Suture for Fascial Closure in Spinal Surgery: A Pilot Study

Wound closure is an integral part of every spinal procedure. Effective and secure wound closure is paramount in the prevention of infection, wound dehiscence and the preservation of cosmesis. Barbed suture technologies such as STRATAFIX™ Symmetric have been studied and are used in a variety of specialties, including obstetrics and orthopedic surgery, but is underutilized in neurosurgery. This study aims to assess the time and rate of closure using STRATAFIX™ Symmetric technology for fascial closure and compare this method to the more traditionally used method of fascial closure using braided absorbable sutures below the epidermis. 20 patients were recruited for the study. 10 patients underwent fascial approximation with braided absorbable sutures and definitive fascial closure with STRATAFIX™ Symmetric. In the control group, fascial closure was completed entirely with interrupted braided absorbable stitches. Patients assigned to STRATAFIX™ Symmetric group had shorter mean time for fascial closure, faster rate of average fascial closure, and lower number of total sutures used. The use of barbed suture technology such as STRATAFIX™ Symmetric may reduce the time to closure in thoracolumbar spine surgery without increasing the risk of adverse events. This pilot study forms the framework for a larger randomized, controlled trial appropriately powered for such an analysis