Mean Exit Time and Survival Probability within the CTRW Formalism

An intense research on financial market microstructure is presently in progress. Continuous time random walks (CTRWs) are general models capable to capture the small-scale properties that high frequency data series show. The use of CTRW models in the analysis of financial problems is quite recent and their potentials have not been fully developed. Here we present two (closely related) applications of great interest in risk control. In the first place, we will review the problem of modelling the behaviour of the mean exit time (MET) of a process out of a given region of fixed size. The surveyed stochastic processes are the cumulative returns of asset prices. The link between the value of the MET and the timescale of the market fluctuations of a certain degree is crystal clear. In this sense, MET value may help, for instance, in deciding the optimal time horizon for the investment. The MET is, however, one among the statistics of a distribution of bigger interest: the survival probability (SP), the likelihood that after some lapse of time a process remains inside the given region without having crossed its boundaries. The final part of the article is devoted to the study of this quantity. Note that the use of SPs may outperform the standard "Value at Risk" (VaR) method for two reasons: we can consider other market dynamics than the limited Wiener process and, even in this case, a risk level derived from the SP will ensure (within the desired quintile) that the quoted value of the portfolio will not leave the safety zone. We present some preliminary theoretical and applied results concerning this topic.Comment: 10 pages, 2 figures, revtex4; corrected typos, to appear in the APFA5 proceeding

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio

Histamine beyond its effects on allergy: Potential therapeutic benefits for the treatment of Amyotrophic Lateral Sclerosis (ALS)

ALS currently remains a challenge despite many efforts in performing successful clinical trials and formulating therapeutic solutions. By learning from current failures and striving for success, scientists and clinicians are checking every possibility to search for missing hints and efficacious treatments. Because the disease is very complex and heterogeneous and, moreover, targeting not only motor neurons but also several different cell types including muscle, glial, and immune cells, the right answer to ALS is conceivably a multidrug strategy or the use of broad-spectrum molecules. The aim of the present work is to gather evidence about novel perspectives on ALS pathogenesis and to present recent and innovative paradigms for therapy. In particular, we describe how an old molecule possessing immunomodulatory and neuroprotective functions beyond its recognized effects on allergy, histamine, might have a renewed and far-reaching momentum in ALS

Activity autocorrelation in financial markets. A comparative study between several models

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Comment: 15 pages, 4 figure

Coupled continuous time random walks in finance

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that generalize the familiar stable models. In this paper, we will review the fundamental theory and present two applications with tick-by-tick stock and futures data.Comment: 7 pages, 2 figures. Paper presented at the Econophysics Colloquium, Canberra, Australia, November 200

Process Evaluation and Continuous Improvement in Community Youth Programs

A method of using process evaluation to provide improvement plans in order to promote community youth programs is described. The core elements of this method include the following: (1) collection and analysis of baseline data, (2) feedback provided to programs describing their strengths and limitations, (3) programs provided with assistance in preparing improvement plans in regard to their baseline data, and (4) follow-up evaluation assessed program changes based on their improvement plans and baseline data. A case study of an inner-city neighborhood youth center is used to demonstrate this method

An Iterative Method Based on Fractional Derivatives for Solving Nonlinear Equations

The theory of fractional order derivatives are almost as old as the integer-order [5]. There are many applications, for example in physics [1], [2], [6], finance [8], [9] or biology [3]. Our aim is not to use fractional order operators to modeling such things, we only will use them as a device to prove a theoretical mathematical statement. In this work our goal is to find a solution numerically for the equation A(u) = f . If we assume that u is time-dependent, then one can do this by finding a stationary solution of the equation ¶tu(t)

Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.Comment: 5 pages, 7 figures, RevTeX, proceedings of APFA-5. V.2: minor typos corrected, 2 references adde

A Process and Outcome Evaluation of Police Working with Youth Programs

A process and outcome evaluation of 10 Police Working with Youth Programs was conducted. Process results indicated that the core components of the programs were consistent with those identified in previous literature as characteristic of quality youth development programs. Outcome results indicated that youth participants reported significantly improved attitudes toward police and social support received from significant, non-familial adults. Two subgroups of youth, most notably minority youth and younger participants in lower grade levels, reported positive changes in their capacity to resist peer pressures. Minority youth reported positive changes in their sense of mastery over stressful life situations. Relationships between core program components and youth outcomes also were examined. Implications of the findings and future process and outcome evaluations of youth programs are discussed

dysferlin in a hyperckaemic patient with caveolin 3 mutation and in c2c12 cells after p38 map kinase inhibition

Dysferlin is a plasma membrane protein of skeletal muscle whose deficiency causes Miyoshi myopathy, limb girdle muscular dystrophy 2B and distal anterior compartment myopathy. Recent studies have reported that dysferlin is implicated in membrane repair mechanism and coimmunoprecipitates with caveolin 3 in human skeletal muscle. Caveolin 3 is a principal structural protein of caveolae membrane domains in striated muscle cells and cardiac myocytes. Mutations of caveolin 3 gene (CAV3) cause different diseases and where caveolin 3 expression is defective, dysferlin localization is abnormal. We describe the alteration of dysferlin expression and localization in skeletal muscle from a patient with raised serum creatine kinase (hyperCKaemia), whose reduction of caveolin 3 is caused by a CAV3 P28L mutation. Moreover, we performed a study on dysferlin interaction with caveolin 3 in C2C12 cells. We show the association of dysferlin to cellular membrane of C2C12 myotubes and the low affinity link between dysferlin and caveolin 3 by immunoprecipitation techniques. We also reproduced caveolinopathy conditions in C2C12 cells by a selective p38 MAP kinase inhibition with SB203580, which blocks the expression of caveolin 3. In this model, myoblasts do not fuse into myotubes and we found that dysferlin expression is reduced. These results underline the importance of dysferlin-caveolin 3 relationship for skeletal muscle integrity and propose a cellular model to clarify the dysferlin alteration mechanisms in caveolinopathies