Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.     

A social network model of investment behaviour in the stock market

To consider the psychological factors that impact market valuation, a model is formulated for investment behaviour of traders whose decisions are influenced by their trusted peers’ behaviour. The model is implemented and several different “trust networks” are tested. Simulation results demonstrate that real life trust networks can significantly delay the stabilisation of a market.     

The risks and returns of stock investment in a financial market

The risks and returns of stock investment are discussed via numerically simulating the mean escape time and the probability density function of stock price returns in the modified Heston model with time delay. Through analyzing the effects of delay time and initial position on the risks and returns of stock investment, the results indicate that: (i) There is an optimal delay time matching minimal risks of stock investment, maximal average stock price returns and strongest stability of stock price returns for strong elasticity of demand of stocks (EDS), but the opposite results for weak EDS; (ii) The increment of initial position recedes the risks of stock investment, strengthens the average stock price returns and enhances stability of stock price returns. Finally, the probability density function of stock price returns and the probability density function of volatility and the correlation function of stock price returns are compared with other literatures. In addition, good agreements are found between them.     

Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices

We analyze 27 house price indices of Las Vegas from June 1983 to March 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real estate bubble, defined as a price acceleration faster than exponential, which is found, however, to be confined to a rather limited time interval in the recent past from approximately 2003 to mid-2004 and has progressively transformed into a more normal growth rate comparable to pre-bubble levels in 2005. There has been no bubble till 2002 except for a medium-sized surge in 1990. In addition, we have identified a strong yearly periodicity which provides a good potential for fine-tuned prediction from month to month. A monthly monitoring using a model that we have developed could confirm, by testing the intra-year structure, if indeed the market has returned to “normal” or if more turbulence is expected ahead. We predict the evolution of the indices one year ahead, which is validated with new data up to September 2006. The present analysis demonstrates the existence of very significant variations at the local scale, in the sense that the bubble in Las Vegas seems to have preceded the more global USA bubble and has ended approximately two years earlier (mid-2004 for Las Vegas compared with mid-2006 for the whole of the USA).     

The co-evolution of cultures,social network communities,and agent locations in an extension of Axelrod’s model of cultural dissemination

We introduce a variant of the Axelrod model of cultural dissemination in which agents change their physical locations, social links, and cultures. Numerical simulations are used to investigate the evolution of social network communities and the cultural diversity within and between these communities. An analysis of the simulation results shows that an initial peak in the cultural diversity within network communities is evident before agents segregate into a final configuration of culturally homogeneous communities. Larger long-range interaction probabilities facilitate the initial emergence of culturally diverse network communities, which leads to a more pronounced initial peak in cultural diversity within communities. At equilibrium, the number of communities, and hence cultures, increases when the initial cultural diversity increases. However, the number of communities decreases when the lattice size or population density increases. A phase transition between two regimes of initial cultural diversity is evident. For initial diversities below a critical value, a single network community and culture emerges that dominates the population. For initial diversities above the critical value, multiple culturally homogeneous communities emerge. The critical value of initial diversity at which this transition occurs increases with increasing lattice size and population density and generally with increasing absolute population size. We conclude that larger initial diversities promote cultural heterogenization, while larger lattice sizes, population densities, and in fact absolute population sizes promote homogenization.     

The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own reservoir, and (ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function, for the off-diagonal peaks of the density matrix, which applies both to common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such a reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix.