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

Statistical Mechanics of Shell Models for 2D-Turbulence

We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager, Hopf and Lee. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy, and from one branch of the formal statistical equilibrium, coincide in these shell models at difference to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence have previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy.Comment: 25 pages + 9 figures, TeX dialect: RevTeX 3.

Variación lateral de facies en el Jurásico basal de la Cordillera Ibérica Central: Origen diagenético temprano y tectónica sinsedimentaria

En este trabajo se realiza el análisis sedimentológico de los materiales del inicio del ciclo Jurásico (Rethiense p.p.-Sinemuriense), pertenecientes a las Fms. Cortes de Tajuña, Lécera y Cuevas Labradas (parte inferior) en un sector de la Cordillera Ibérica central, situado en la Sierra de Arcos. Las facies se han agrupado en tres grandes tipos: yesos-anhidritas con intercalación de dolomías, brechas (con clastos evaporíticos y con clastos dolomíticos) y dolomías masivas oquerosas, correspondientes a los subambientes de sebja costera y llanura intermareal, desarrollados en una plataforma interna. Las brechas de disolución tienen un origen sinsedimentario y diagenético temprano y provienen de la disolución de nódulos y niveles de evaporitas intercalados en las dolomías. Las evaporitas son muy potentes en las zonas más subsidentes y se interdigitan lateralmente con brechas de disolución, lo que muestra un cambio gradual en el ambiente de sedimentación. La presencia de facies de evaporitas o de facies de brechas es función de la existencia de áreas supramareales, con aguas sobresaturadas. La variación de potencia observada dentro de la Fm. Cortes de Tajuña es un rasgo original del depósito y está controlada por la subsidencia diferencial y no por la disolución tardía de los niveles evaporíticos.A sedimentological analysis has been carried out in the uppermost Raethian-Sinemurian, Cortes de Tajuña, Lécera and Cuevas Labradas (lower part) Fms., in the outcrops of the Sierra de Arcos (central Iberian Chain, NE Spain). Three facies have been distinguished: gypsum-anhydrite with dolomitic intercalations, breccias (with evaporitic and dolomitic clasts) and massive dolomites. These facies were deposited in inner platform areas, ranging from shallow sabkha to intertidal flat environments. Breccias were originated by dissolution during the early stages of the diagenesis. The presence of evaporites reflects the development of supratidal areas, oversaturated in salts. Thick evaporites successions change laterally to breccias, showing a gradual environmental transition. Overall thickness variation in the uppermost Raethian-Hettangian units was controlled by local basin subsidence due to normal faulting, rather than late burial dissolution of evaporitic levels

Macroscopic chaos in globally coupled maps

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, these macroscopic behaviours. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at hydrodynamical level is then possible, even in the absence of the explicit equations for the time evolution of the macroscopic observables.Comment: 24 pages revtex, 9 figures included. Improved version also with 1 figure and some references adde

Behavior of heuristics and state space structure near SAT/UNSAT transition

We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is significantly simpler, while similar to, walksat or Focused Metropolis Search. We show that ASAT solves instances as large as one million variables in linear time, on average, up to 4.21 clauses per variable for random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd

Inverse Ising inference using all the data

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of $l_1$-regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.Comment: 5 pages, 2 figures. Accepted versio

Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil's staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.Comment: 12 pages, LaTe

El Pliensbachiense de la Rama Aragonesa de la Cordillera Ibérica: Análisis de facies y establecimiento de secuencias

The Pliensbachian of the Aragonese branch of the Iberian Chain is represented by Almonacid de la Cuba, Cerro del Pez and Barahona formations. These sediments are constituted by marls and limestone organized in shallowingupward sequences. All of them are represented in the lower part by marls and mudstone that change to wackestone and packstone. The top of the sequence is a ferruginous crust, generally bioturbated. This represents the decrease in the sedimentation velocity and a shallowing event. The sediments were deposited in a carbonate ramp, changing from middle to outer environments. The most shallowing facies were located in the south, where there is an evidence of the developing of reefal facies. The deeper facies were deposited in the north, corresponding to open environments. This work shows the correlation of six thirdorder shallowing upward sequences in the Pliensbachian sediments. The origin of these sequences is related to sea level oscillations and conditioned by autocyclic processes

"Locally homogeneous turbulence" Is it an inconsistent framework?

In his first 1941 paper Kolmogorov assumed that the velocity has increments which are homogeneous and independent of the velocity at a suitable reference point. This assumption of local homogeneity is consistent with the nonlinear dynamics only in an asymptotic sense when the reference point is far away. The inconsistency is illustrated numerically using the Burgers equation. Kolmogorov's derivation of the four-fifths law for the third-order structure function and its anisotropic generalization are actually valid only for homogeneous turbulence, but a local version due to Duchon and Robert still holds. A Kolomogorov--Landau approach is proposed to handle the effect of fluctuations in the large-scale velocity on small-scale statistical properties; it is is only a mild extension of the 1941 theory and does not incorporate intermittency effects.Comment: 4 pages, 2 figure