A linear decision analysis model of optimal portfolio investments

The paper develops a decision analysis model to determine the optimal portfolio investment under uncertainty. The model extends Sharpe'a simplified model by assuming a stochastic linear equation system that relates the random returns of various risky assets to certain stochastic and uncontrollable exogenous variables and specifies that the investor has a subjective joint probability distribution describing the investor's belief in the probable values of the linear system's parameters. Decision rules are derived and four numerical examples are presented to illustrate the decision process. It is found that both the number of stochastic and uncontrollable exogenous variables that explain the random returns and correlated disturbances (non-diagonalily) exert substantial effects on optimal portfolio decisions of the investor.