Asset Price Dynamics with Local Interactions under Heterogeneous Beliefs

This paper investigates the effect of network structure on the asset price dynamics. We propose a simple present value discounted asset pricing model with heterogeneous agents. Every period the agents choose a predictor of the future price on the basis of past performance of their own and alternative strategies and form their demands for a risky asset. The information about the performance of an alternative strategy is available only locally from the directly connected agents. Using the rewiring procedure we produce four types of commonly considered networks: a fully connected network, a regular lattice, a small world, and a random network. The results show that the network structure influences asset price dynamics in terms of the region of stability and volatility. This is mostly due to the different speed of information transmission in the different networks.

Non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models

New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogenuity dimensions. The nonpolynomial densities with logarithmics behaviour are presented as an example. The special attention is paid for the singular case $(\gamma=1)$ for which we found new non homogenious solutions expressed in terms of the elementary functions.Comment: 11 pages, 1 figur