Kinetic model for asset allocation with strategy switching

Abstract

The kinetic theory is employed to study the changes in the amount of wealth invested in two types of risky assets when investors switch their trading strategies. Investors in the market are assumed to possess nonnegative wealth and opt to allocate a portion of their wealth into two types of risky assets. A Boltzmann model, which includes strategy switching and interaction probability, is utilized to investigate the evolution of the amount of wealth invested in risky assets and the number of investors using fundamentalist and chartist strategies. We employ the asymptotic procedure method to derive the Fokker-Planck equations from the Boltzmann model. The resulting stationary solution of these equations sheds light on the effects of strategy switching on the evolution of the amount of wealth invested in risky assets, as well as how investor interactions influence the number of investors employing different strategies.