Before revision:  We then compare the intra-personal equilibrium strategy in the case of \alpha=1/2, namely under median maximization , to some other strategies and apply it to explain why more wealthy people invest more precentage of wealth in risky assets . Finally, we extend our model to account for multiple terminal time .
After revision:  We then compare the intra-personal equilibrium strategy in the case of \alpha=1/2, namely under median maximization , to some other strategies and apply it to explain why more wealthy people invest more precentage of wealth in risky assets .