A behavioral stock market model

Stock exchanges are modeled as nonlinear closed-loop systems where the plant dynamics is defined by known stock market regulations and the actions of agents are based on their beliefs and behavior. The decision of the agents may contain a random element, thus we get a nonlinear stochastic feedback system. The market is in equilibrium when the actions of the agents reinforce their beliefs on the price dynamics. Assuming that linear predictors are used for prediction of the price process, a stochastic approximation procedure for finding market equilibrium is described. The proposed procedure is analyzed using the theory of Benveniste et al. (Adaptive algorithms and stochastic approximations. Springer, Berlin, 1990). A simulation result is also presented.     

The European options hedge perfectly in a Poisson-Gaussian stock market model

It is shown that n + 1 European call options written on a stock S with different strike prices (or the stock and n calls) are non-redundant assets in a model for the stock driven by a Brownian motion and n independent Poisson processes. That extends the result obtained for n = 1 by Pham and implies that the proposed model can price and perfectly hedge any integrable derivative on S.     

Stochastic resonance in an interacting-agent model of stock market

On the specific example of an interacting-agent model of speculative activity we have demonstrated that stochastic resonance (SR), where an increase in the noise (market volatility) increases the signal-to-noise ratio (SNR) describing the response to global periodic investment bias, can occur in the stock market. This phenomenon may be in principle utilized by market traders.     

Nonlinear dynamic effects in automotive clutches

Dynamic effects appearing in the dry friction clutches are very complex. The reason for this is the usual design of the clutches including complex two dimensional friction, unilateral contacts and nonlinear springs. The final quality of the clutch system for a customer depends among other criteria on the awareness of dynamic effects, which can affect functioning and comfort negatively. One of the usual nonlinear dynamic effects in the friction clutch is presented in this work. That is the problem of dynamic disengagement which can cause significant safety problems. First of all the global nonlinear dynamic behavior is considered roughly by means of an analytical approach. Secondly a MBS-model, which includes not only the nominal design of the clutch system but also dispersion of several parameters, is used in order to identify the influence of the asymmetry on the dynamic behavior. Analytical and numerical results are compared with measurements. Finally a possible solution of the considered problem is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Allee effects in a discrete-time SIS epidemic model with infected newborns

We extend the framework of Rios-Soto et al. (Contemporary Mathematics, 2006, 410, 297) to include both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number ?₀, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This is in contrast to the recent observations of Franke and Yakubu, that the demographic dynamics can be chaotic while the infective dynamics are oscillatory and non-chaotic in periodically-forced SIS epidemic models (Mathematical Biosciences, 2006, 204, 68).     

Fluctuations of interface statistical physics models applied to a stock market model

In this paper, applying the theory of fluctuations of the interfaces for statistical physics lattice models, we construct a financial model and use this financial model to describe the behavior or fluctuations of a stock price process in a stock market. By using the methods of statistical physics and under some conditions, we show that the finite dimensional distribution of a normalized random process for this financial model converges to the corresponding distribution of the Black–Scholes model.     

Pure equilibria in a simple dynamic model of strategic market game

We present a discrete model of two-person constant-sum dynamic strategic market game. We show that for every value of discount factor the game with discounted rewards possesses a pure stationary strategy equilibrium. Optimal strategies have some useful properties, such as Lipschitz property and symmetry. We also show value of the game to be nondecreasing both in state and discount factor. Further, for some values of discount factor, exact form of optimal strategies is found. For β less than , there is an equilibrium such that players make large bids. For β close to 1, there is an equilibrium with small bids. Similar result is obtained for the long run average reward game.     

A simple finite-difference stock market model involving intrinsic value

We suggest a deterministic delay difference model for the time series of the closing stock price and the intrinsic value of the stock. The most important new feature of this model is the equation describing the evolution of the intrinsic value. We present a general solution for the model in question and study the stability of the stationary points. Comparison with the real-world data shows that upon a suitable choice of parameters our model exhibits a behavior reasonably similar to that of the real stock, at least for shorter time ranges (those of several weeks).     

Optimal partial hedging in a discrete-time market as a knapsack problem

We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be treated as so called knapsack problems, which are a widely researched subject in linear programming. This observation gives us better understanding of the problem of optimal hedging in discrete time.     

Complex dynamic behaviors of a discrete-time predator-prey system

The dynamics of a discrete-time predator-prey system is investigated in detail in this paper. It is shown that the system undergoes flip bifurcation and Hopf bifurcation by using center manifold theorem and bifurcation theory. Furthermore, Marotto''s chaos is proved when some certain conditions are satisfied. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-6, 7, 8, 10, 14, 18, 24, 36, 50 orbits, attracting invariant cycles, quasi-periodic orbits, nice chaotic behaviors which appear and disappear suddenly, coexisting chaotic attractors, etc. These results reveal far richer dynamics of the discrete-time predator-prey system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method.     

Computational study of the US stock market evolution: a rank correlation-based network model

This paper presents a computational study of global characteristics of the US stock market using a network-based model referred to as the market graph. The market graph reflects similarity patterns between stock return fluctuations via linking pairs of stocks that exhibit “coordinated” behavior over a specified period of time. We utilized Spearman rank correlation as a measure of similarity between stocks and considered the evolution of the market graph over the recent decade between 2001–2011. The observed market graph characteristics reveal interesting trends in the stock market over time, as well as allow one to use this model to identify cohesive clusters of stocks in the market.     

Nonlinear dynamic analysis of viscoelastic beams using a fractional rheological model

The paper presents quasi-static analysis, classical and fractional dynamic analysis of a simply supported viscoelastic beam subjected to uniformly distributed load, where the Riemann–Liouville fractional derivative is of the order ν ∈ (0, 1). A comparative study of the results obtained for a classical and fractional Zener model using the techniques of Laplace transform, Bessel functions theory and binomial series is achieved. The graphic representations show how the existence of fractional derivative in the selected rheological model influences the dynamic response of the structure. This paper provides a theoretical basis for researchers who want to choose a mathematical model that will precisely fit with a particular experimental model.     

Prescribed performance of discrete-time controller based on the dynamic equivalent data model

The equivalent model of a class of unknown discrete-time systems is developed by data-driven approach and fuzzy rules inference network when plant’s control direction can vary for both positive and negation and zero at the dead-zone. The convergence of the modeling error is guaranteed by the proposed learning algorithm. By using the equivalent model, the prescribed performance controller is established when the tracking error is preserved inside the designed boundary at both transient and steady states. The performance of the proposed scheme is validated by theoretical and practical results.     

Persistence in a discrete-time,stage-structured epidemic model

Discrete-time SI and SIR epidemic models, formulated by Emmert and Allen [J. Differ. Equ. Appl., 10 (2004), pp. 1177–1199] for the spread of a fungal disease in a structured amphibian host population, are analysed. Criteria for persistence of the population as well as for persistence of the disease are established. Global stability results for host extinction and for the disease-free equilibrium are presented.     

Convex hedging of non-superreplicable claims in discrete-time market models

All of the papers written so far deal with efficient hedging of contingent claims for which superhedging exists. The goal of this paper is to investigate the convex hedging of contingent claims for which superhedging does not exist. Without superhedging assumption it is still possible to prove the existence of a solution, but one cannot obtain structure of the solution using techniques known so far. Therefore, we develop a new approximative approach to deduce structure of the solution in case of non-superreplicable claims.     

中国股票市场的日历效应分析

本文以上证指数和深证指数为代表 ,对中国股票市场的日历效应进行实证分析 .主要从以下三个方面加以讨论 :收益率和交易量的均值及方差的日历特征 ;收益率日历特征的相关分析 ;收益率周内各日的转移概率特性     

Optimal selling time in stock market over a finite time horizon

In this paper, we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0, T ], where the stock price is modelled by a geometric Brownian motion and the ’closeness’ is measured by the relative error of the stock price to its highest price over [0, T ]. More precisely, we want to optimize the expression: where (V t ) t≥0 is a geometric Brownian motion with constant drift α and constant volatility σ > 0, M t = max Vs is the running maximum of the stock price, and the supremum is taken over all possible stopping times 0 ≤τ≤ T adapted to the natural filtration (F t ) t≥0 of the stock price. The above problem has been considered by Shiryaev, Xu and Zhou (2008) and Du Toit and Peskir (2009). In this paper we provide an independent proof that when α = 1 2 σ 2 , a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the moment when the stock price hits its maximum price so far. Besides, when α > 1 2 σ 2 , selling the stock at the terminal time T is the unique optimal selling strategy. Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping ρτ of a stopping time τ to the optimal stopping strategy arisen in the classical "Secretary Problem".     

中国股票市场收益率分布曲线的实证

股票价格行为的随机理论认为市场收益服从正态分布 ,但在现实中这一假设不一定成立 ,市场收益率更多地呈现出偏离正态分布的形式。本文检验中国市场的收益率分布形态。