Abstract: This paper addresses a dynamic portfolio investment problem. It discusses how we can dynamically choose candidate assets, achieve the possible maximum revenue and reduce the risk to the minimum level. The paper generalizes Markowitz’s portfolio selection theory and Sharpe’s rule for investment decision. An analytical solution is presented to show how an institutional or individual investor can combine Markowitz’s portfolio selection theory, generalized Sharpe’s rule and Value-at-Risk (VaR) to find candidate assets and optimal level of position sizes for investment (dis-investment). The result shows that the generalized Markowitz’s portfolio selection theory and generalized Sharpe’s rule improve decision making for investment.

Key words: Portfolio investment, Value-at-Risk (VaR), Generalized Sharpe’s rule

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