Stochastic Rules Research Articles

Dynamical behavior of price forecasting in structures of group correlations

We investigate the prediction of the future prices from the structures and the networks of the companies in special financial groups. After the financial group network has been constructed from the value of the high cross-correlation, each company in a group is simulated and analyzed how it buys or sells stock is anaylzed and how it makes rational investments is forecasted. In the shortmemory behavior rather than the long-memory behavior, each company among a group can make a rational investment decision by using a stochastic evolution rule in the financial network. In particular, we simulate and analyze the investment situation in connection with the empirical data and the simulated result.

Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance

We develop and implement linear formulations of convex stochastic dominance relations based on decreasing absolute risk aversion (DARA) for discrete and polyhedral choice sets. Our approach is based on a piecewise-exponential representation of utility and a local linear approximation to the exponentiation of log marginal utility. An empirical application to historical stock market data suggests that a passive stock market portfolio is DARA stochastic dominance inefficient relative to concentrated portfolios of small-cap stocks. The mean-variance rule and Nth-order stochastic dominance rules substantially underestimate the degree of market portfolio inefficiency because they do not penalize the unfavorable skewness of diversified portfolios, in violation of DARA. This paper was accepted by James Smith, decision analysis.

Weighted Almost Stochastic Dominance: Revealing the Preferences of Most Decision Makers in the St. Petersburg Paradox

There are instances where “most” individuals prefer one prospect over another in practice, but such preferences are not revealed by conventional stochastic dominance rules. Almost stochastic dominance aims to reveal such preferences. However, almost stochastic dominance does not reveal the preferences observed in the St. Petersburg paradox. In this paper, we generalize the conditions of almost stochastic dominance by introducing a weighting function and illustrate how our proposed condition reveals the preferences of most individuals in the St. Petersburg paradox.

Coarse-graining the Dynamics of Ideal Branched Polymers

We define a class of local stochastic rewrite rules on directed site trees. We give a compact presentation of (often countably infinite) coarse-grained differential systems describing the dynamics of these rules in the deterministic limit, and study in a simple case finite approximations based on truncations to a certain size. We show an application to the modelling of the dynamics of sugar polymers.

A method for discrete stochastic MADM problems based on the ideal and nadir solutions

Many real life decision making problems can be modeled as discrete stochastic multi-attribute decision making (MADM) problems. A novel method for discrete stochastic MADM problems is developed based on the ideal and nadir solutions as in the classical TOPSIS method. In a stochastic MADM problem, the evaluations of the alternatives with respect to the different attributes are represented by discrete stochastic variables. According to stochastic dominance rules, the probability distributions of the ideal and nadir variates, both are discrete stochastic variables, are defined and determined for a set of discrete stochastic variables. A metric is proposed to measure the distance between two discrete stochastic variables. The ideal solution is a vector of ideal variates and the nadir solution is a vector of nadir variates for the multiple attributes. As in the classical TOPSIS method, the relative closeness of an alternative is determined by its distances from the ideal and nadir solutions. The rankings of the alternatives are determined using the relative closeness. Examples are presented to illustrate the effectiveness of the proposed method. Through the examples, several significant advantages of the proposed method over some existing methods are discussed.

A new stochastic cellular automata model for traffic flow simulation with drivers’ behavior prediction

In this work, we introduce a novel, flexible and robust traffic flow cellular automata model. Our proposal includes two important stages that make possible the consideration of different profiles of drivers’ behavior in a simple way. We first consider the motion expectation of vehicles that are in front of each driver. Secondly, we define how a specific vehicle decides to get around, considering the foreground traffic configuration. Our model uses stochastic rules for both situations, using the Probability Density Function of the Beta Distribution to model three drivers’ behavior, adjusting different parameters of the Beta Distribution for each one.

Generalized Almost Stochastic Dominance

Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. While the idea behind almost stochastic dominance is quite promising, it has not caught on in practice. Implementation issues and inconsistencies between integral conditions and their associated utility classes contribute to this situation. We develop generalized almost second-degree stochastic dominance and almost second-degree risk in terms of the appropriate utility classes and their corresponding integral conditions, and extend these concepts to higher degrees. We address implementation issues and show that generalized almost stochastic dominance inherits the appealing properties of stochastic dominance. Finally, we define convex generalized almost stochastic dominance to deal with risk-prone preferences. Generalized almost stochastic dominance could be useful in decision analysis, empirical research (e.g., in finance), and theoretical analyses of applied situations.

English

This paper focuses on Mean-Gini (MG) method for optimum portfolio selection. The MG framework, introduced by Shalit and Yitzhaki, is an attractive alternative as it is consistent with stochastic dominance rules regardless of the probability distributions of asset returns. Therefore, a MG framework is similar to a corresponding Mean-Variance (MV) framework in that it also uses two summary statistics-the mean and a measure of dispersion to characterize the distribution of a risky prospect. The goal of this paper is to test MG strategy, based on Moroccan financial market data from turbulent market period of the years 2011, 2012, 2013 and 2014. In addition, those outcomes are explicitly tested in terms of Value-at-risque (VaR). The results show that MG strategy is profitable for investors. Moreover, we consider MG strategy to be safer in turbulent times.   Key words: Diversification, MG, mean-variance, Morrocan financial market, portfolio selection, value-at-risk.

A spiking neural network based on the basal ganglia functional anatomy

We introduce a spiking neural network of the basal ganglia capable of learning stimulus–action associations. We model learning in the three major basal ganglia pathways, direct, indirect and hyperdirect, by spike time dependent learning and considering the amount of dopamine available (reward). Moreover, we allow to learn a cortico-thalamic pathway that bypasses the basal ganglia. As a result the system develops new functionalities for the different basal ganglia pathways: The direct pathway selects actions by disinhibiting the thalamus, the hyperdirect one suppresses alternatives and the indirect pathway learns to inhibit common mistakes. Numerical experiments show that the system is capable of learning sets of either deterministic or stochastic rules.

Global path-following control of underactuated ships under deterministic and stochastic sea loads

SUMMARYThis paper presents a new method to design global path-following controllers for underactuated ships under both deterministic and stochastic sea loads. The path-following errors are first interpreted in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov's direct methods. Weak and strong nonlinear Lyapunov functions are introduced to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule, and to guarantee boundedness of the sway velocity. Potential projection functions are introduced to design update laws that provide bounded estimates of the mean values and covariances of the disturbances. Simulations are included to illustrate the effectiveness of the proposed approach.

Differential growth of wrinkled biofilms.

Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and studied. Gene expression regulates cell division and differentiation, which affect the biofilm architecture. Mechanical and chemical processes shape the resulting structure. We gain insight into the interplay between cellular and mechanical processes during biofilm development on air-agar interfaces by means of a hybrid model. Cellular behavior is governed by stochastic rules informed by a cascade of concentration fields for nutrients, waste, and autoinducers. Cellular differentiation and death alter the structure and the mechanical properties of the biofilm, which is deformed according to Föppl-Von Kármán equations informed by cellular processes and the interaction with the substratum. Stiffness gradients due to growth and swelling produce wrinkle branching. We are able to reproduce wrinkled structures often formed by biofilms on air-agar interfaces, as well as spatial distributions of differentiated cells commonly observed with B. subtilis.

On a non-linear stochastic dynamic circuit using Stratonovich differential

The stochastic differential equation is the standard approach to analyse dynamic circuits in noisy environments. Ignoring non-linearity as well as inaccurate stochastic interpretations will have influence on the state estimation procedure and control of dynamic circuits. This paper intends to develop the mathematical theory of a non-linear time-varying stochastic system, a noisy sampling mixer, an appealing non-linear stochastic dynamic circuit of digital communication systems. In this paper, we formalize the sampling mixer that assumes the structure of a non-linear time-varying Stratonovich SDE (Stochastic Differential Equation) in lieu of a bilinear time-varying Itô SDE. Subsequently, the theory of the noise-influenced sampling mixer is achieved using the following influential results of stochastic processes: (i) the Itô–Stratonovich integral relationship and (ii) stochastic differential rules. After utilising these two results of stochastic processes, we derive the conditional moment evolutions of the sampling mixer.Importantly, the noise analysis of this paper confirms the consensus on the Itô–Stratonovich calculi dilemma as well as accounts for square non-linearity. This paper is useful for applied mathematicians as well as stochastic dynamists looking for applications of Stratonovich stochastic methods to potential practical problems, which are relatively very scarce in the literature.

Weak Convergence Rate of SDE with Stochastic Integration by Trapezoidal Rule

The Heston stochastic volatility model is one of the most fundamental models in mathematical finance. In the literature, numerous efficient simulation methods have been proposed, however, there is no analytical weak convergence rate obtained, which is a long-standing problem. In this article, we derive the weak convergence rate of a time-discrete scheme for the Heston stochastic volatility model, that employ the stochastic trapezoidal rule to discretize the logarithmic asset process, and simulate the variance process exactly. The test function we consider for the error criterion can be any polynomials of the logarithmic asset process. We show that the analytical weak convergence rate is two in all parameter regimes. The result is consistent with the standard rate of the stochastic trapezoidal rule, although the coefficient of the model does not satisfy the global Lipschitz condition. To prove it, we introduce a novel analysis in a more general context. In the majority of literature, the analysis is based on assumptions on coefficients of SDEs, whereas we impose no direct conditions on the coefficient. Instead, we transfer the error analysis to that of a classical trapezoidal rule on a deterministic integral, on which we make some mild assumptions.

Hybrid Modelling in Cell Biology

Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a (complex) phenomenon that cannot be described in a standard homogeneous way. This is often the case with multiscale phenomena, where the most macroscopic part usually have a continuous nature (chemical fields, concentration of populations, etc) whereas the microscopic part reveals the discrete nature of its elements (particles, individuals, etc). Consequently, hybrid models usually take the form of a system of partial differential equations (PDEs, e.g. for reaction-diffusion equations), or a system of ordinary differential equations (ODEs, e.g. for kinetics reactions), coupled with an individual based model, such as a cellular automaton (CA) or an agent-based model (ABM) both operating from a set of either deterministic or stochastic rules. In a wider sense, hybrid modelling corresponds to any mixed approaches and this includes, for example, the coupling of deterministic and stochastic models which can either be discrete or continuous. Back to the nineties, mathematical biology was mostly dominated by the use of PDEs and ODEs, i.e. continuous models of equations. The rise of discrete approaches occurred from this period and it coincides with the evolution of processors and the resulting computing capabilities of desktop computers that have permitted to simulate scientifically relevant discrete models. The shift from pure mathematical approaches (mostly continuous) to more computational approaches (mostly discrete) is observed from those years, and correspond to the emergence of a still growing number of hybrid models. We observe that as a consequence mathematical biology has, through the recent years, been overwhelmed by computational biology. Multiscale modelling, and hence the development of hybrid models, was especially stimulated in the context of systems biology. This consists in studying a phenomenon as a whole, requiring the integration of the spatial scales from molecules (nanometre) to organs (centimetre) and temporal scales from reaction kinetics (microsecond) to developmental scales (months to years), rather than considering the phenomenon at the different scales independently, which would provide too little insights and make no sense in modern biology. In cell biology, hybrid modelling has permitted to reach a higher level of understanding between experimentalists and theoreticians, since the level of abstraction in the discrete part of the models is often lower. It usually consists in the definition of a set of rules that are based on direct experimental observations or measurements. It then makes it easier to compare both qualitatively and

Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.

Often, sample size is not fixed by design. A key example is a sequential trial with a stopping rule, where stopping is based on what has been observed at an interim look. While such designs are used for time and cost efficiency, and hypothesis testing theory has been well developed, estimation following a sequential trial is a challenging, still controversial problem. Progress has been made in the literature, predominantly for normal outcomes and/or for a deterministic stopping rule. Here, we place these settings in a broader context of outcomes following an exponential family distribution and, with a stochastic stopping rule that includes a deterministic rule and completely random sample size as special cases. It is shown that the estimation problem is usually simpler than often thought. In particular, it is established that the ordinary sample average is a very sensible choice, contrary to commonly encountered statements. We study (1) The so-called incompleteness property of the sufficient statistics, (2) A general class of linear estimators, and (3) Joint and conditional likelihood estimation. Apart from the general exponential family setting, normal and binary outcomes are considered as key examples. While our results hold for a general number of looks, for ease of exposition, we focus on the simple yet generic setting of two possible sample sizes, N=n or N=2n.

Consensus states of local majority rule in stochastic process

Abstract A sufficient condition for a network system to reach a consensus state of the local majority rule is shown. The influence of interpersonal environment on the occurrence probability of consensus states for Watts–Strogatz and scale-free networks with random initial states is analyzed by numerical method. We also propose a stochastic local majority rule to study the mean first passage time from a random state to a consensus and the escape rate from a consensus state for systems in a noisy environment. Our numerical results show that there exists a window of fluctuation strengths for which the mean first passage time from a random to a consensus state reduces greatly, and the escape rate of consensus states obeys the Arrhenius equation in the window.

A modeling approach of the chemostat

Population dynamics and in particular microbial population dynamics, though intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. In these type of models, populations are represented by continuous population sizes or densities usually with deterministic dynamics.Over the last decades, alternate individual-based models have been proposed where population is explicitly represented as a set of individuals. These may include stochastic dynamics or stochastic rules. With reference to the last class of models we can also associate pure jump processes where the population is described as a discrete population size with stochastic discrete event evolutions.In the first class of models the population dynamics and its representation may be viewed respectively as deterministic and continuous, in the second class they may be viewed respectively as stochastic and discrete.In this present work, we present a modeling approach that bridges the two representations. This link can be mathematically described as a functional law of large numbers in high population size asymptotics. These results suggest new strategies of modeling and simulation. We illustrate this approach on the modeling of the chemostat.

Almost expectation and excess dependence notions

This paper weakens the expectation dependence concept due to Wright (Theory Decis 22:111–124, 1987) and its higher-order extensions proposed by Li (J Econ Theory 146:372–391, 2011) to conform with the preferences generating the almost stochastic dominance rules introduced in Leshno and Levy (Manag Sci 48:1074–1085, 2002). A new dependence concept, called excess dependence is introduced and studied in addition to expectation dependence. This new concept coincides with expectation dependence at first-degree but provides distinct higher-order extensions. Three applications, to portfolio diversification, to the determination of the sign of the equity premium in the consumption-based CAPM, and to optimal investment in the presence of a background risk, illustrate the usefulness of the approach proposed in the present paper.

Efficient deformation algorithm for plasmid DNA simulations.

BackgroundPlasmid DNA molecules are closed circular molecules that are widely used in life sciences, particularly in gene therapy research. Monte Carlo methods have been used for several years to simulate the conformational behavior of DNA molecules. In each iteration these simulation methods randomly generate a new trial conformation, which is either accepted or rejected according to a criterion based on energy calculations and stochastic rules. These simulation trials are generated using a method based on crankshaft motion that, apart from some slight improvements, has remained the same for many years.ResultsIn this paper, we present a new algorithm for the deformation of plasmid DNA molecules for Monte Carlo simulations. The move underlying our algorithm preserves the size and connectivity of straight-line segments of the plasmid DNA skeleton. We also present the results of three experiments comparing our deformation move with the standard and biased crankshaft moves in terms of acceptance ratio of the trials, energy and temperature evolution, and average displacement of the molecule. Our algorithm can also be used as a generic geometric algorithm for the deformation of regular polygons or polylines that preserves the connections and lengths of their segments.ConclusionCompared with both crankshaft moves, our move generates simulation trials with higher acceptance ratios and smoother deformations, making it suitable for real-time visualization of plasmid DNA coiling. For that purpose, we have adopted a DNA assembly algorithm that uses nucleotides as building blocks.

Stochastic evolution equations within the context of both the Hamiltonian and Lagrangian formalisms

It is proved that it is possible to obtain continuum deterministic and stochastic evolution equations from a set of discrete stochastic rules after an average over realizations and over near neighbors or coarse graining on the dynamical variables, respectively. Examples are given that allow us to find the Hamilton evolution equation for the dynamical variables and the Euler evolution equation for the Lagrangian of the system with additive noises.