Related papers: A second-order stock market model
The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this,…
This work models the interconnection of company's investment managers' representations and the market attraction of its shares. The models that reflect the connection of the company's market effectiveness indices and parameters of its…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market…
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive…
Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the…
We consider likelihood-based two-step estimation of latent variable models, in which just the measurement model is estimated in the first step and the measurement parameters are then fixed at their estimated values in the second step where…
The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights versus ranks. For the US stock market, it is linear on a…
This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…
A new notion is introduced of matrix order indices which relate the matrix norm and its trace. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…