On optimal investiment strategies

Suppose an investor has a fixed decision horizon and an appropriate utility function for measuring his or her utility of wealth. If there are only two investment vehicles, a risky and a risk-free asset, then the optimal investment strategy is such that, at any time, the amount invested in the risky asset must be the product of his or her “current risk tolerance” and the risk premium on the risky asset, divided by the square of the diffusion coefficient of the risky asset. In the case of more than one risky asset, the optimal investment strategy is similar, with the ratios of the amounts invested in the different risky assets being constant over time.