Short distance signatures in Cosmology: Why not in Black Holes?

Current theoretical investigations seem to indicate the possibility of observing signatures of short distance physics in the Cosmic Microwave Background spectrum. We try to gain a deeper understanding on why all information about this regime is lost in the case of Black Hole radiation but not necessarily so in a cosmological setting by using the moving mirror as a toy model for both backgrounds. The different responses of the Hawking and Cosmic Microwave Background spectra to short distance physics are derived in the appropriate limit when the moving mirror mimics a Black Hole background or an expanding universe. The different sensitivities to new physics, displayed by both backgrounds, are clarified through an averaging prescription that accounts for the intrinsic uncertainty in their quantum fluctuations. We then proceed to interpret the physical significance of our findings for time-dependent backgrounds in the light of nonlocal string theory.Comment: 10 pages, 2 figures, REVTeX 4 styl

Asset Price and Wealth Dynamics in a Financial Market with Heterogeneous Agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalits and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors have CRRA utility, so that their optimal demand for the risky asset depends on wealth. A market maker is assumed to adjust the price at the end of each trading period, on the basis of the excess demand and according to particular stabilization policies. The model results in a three-dimensional nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents' behavior (in particular the risk aversion coefficient and the chartist extrapolation parameter) as well as on the initial condition (in particular the initial wealth shares of fundamentalists and chartists). It is also shown that the for wide ranges of the parameters a (locally) stable fundamental steady state may coexist with a stable "nonfundamental" steady state, where price grows faster than the fundamental and only chartists survive in the long-run. In such cases, the role played by the initial condition is analysed by means of numerical investigations and graphical representation of the basins of attraction. Other dynamic scenarios include limit cycles, periodic orbits or more complex attractors, where in general both types of agents survive in the long run, with time varying wealth fractions.heterogeneous agents; financial market dynamics; wealth dynamics; coexisting attractors

A Dynamic Analysis of Speculation Across Two Markets

A discrete time model of a financial market is proposed, where the time evolution of asset prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists. Each group allocates its wealth between a risky asset (stock) and an alternative asset (bond), and the two groups have heterogeneous expectations about returns. We assume that chartists compute expected returns by extrapolating past price changes, while fundamentalists form their expectations on the basis of their superior knowledge of fundamentals. Under the assumption that agents have CRRA utility, investors' optimal demand for each asset depends on their wealth, and this results in growing price and wealth processes. The time evolution of the prices is modeled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an off-setting long or short position. The market maker is assumed to adjust the price, in each period, partly on the basis of the excess demand and partly according to a particular market stabilization policy. The model is reduced to a high dimensional nonlinear discrete-time dynamical system with growing prices and wealth. Although the model is nonstationary, suitable changes of variables lead to a stationary model where the dynamic variables are actual and expected returns, fundamental/price ratios, and wealth proportions of chartists and fundamentalists. The steady states and other invariant sets of the model are determined, and important global dynamic phenomena are studied via numerical techniques. Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series.