Social Behaviour of Agents: Capital Markets and Their Small Perturbations

Abstract

We study social behaviour of agents on capital markets when these are perturbed by small perturbations. We use the mean field method. Social behaviour of agents on capital markets is described: volatility of the market, aversion constant and equilibrium states are discussed. Relaxation behaviour of agents on the capital market is studied. Equation of motion for the agent average number is of the relaxation type. Development of the group of agents in the states corresponding to minimum of the aim function is either linear either exponentially damped. There exist characteristic volatility constants $ V_{c3} $ and $ V_{c3} $. The constant b of verification of information contribution to the aversion constant A and the $ A_{0} $ constant of aversion are distinguishing three types of dependencies of the minimum of the aim function on the expected volatility EV and on the expected returns E. Arbitrage trades and group forces lead the group into the equilibrium state. Verification of information intensity influences return back to the equilibrium state. The linear in time damping to the equilibrium state is characterized with the characteristic time $ T_{3}$ and $ T_{6} $, the exponential with a characteristic time $ \tau $. Their dependence on the expected volatility, on the expected profit and characteristics of agents is discussed.