Portfolio insurers and constant weight traders: who will survive?

We consider the dynamics of asset prices and wealth in an exchange economy with long-lived assets where agents adopt different portfolio strategies: one agent allocates wealth according to the Constant Weight Strategy while the other follows a Portfolio Insurance Strategy. In a Lucas’ tree setting, assuming a binomial model for the dividend process, we provide conditions for survival and (relative) dominance of agents and discuss them in terms of the expected log-return of the risky asset. Both strategies survive for low expected log-returns, while both strategies dominate, but on different paths, for high expected log- returns. We show that the portfolio insurance strategy plays a stabilizing effect on the market volatility.