Optimal dynamic portfolio selection with earnings-at-risk
The paper deals with a continuous-time portfolio selection problem on a Black-Scholes type financial market setting. Intead of the variance in the mean-variance analysis, a new measure of risk is considered here. It is called earnings-at-risk, and measures risk relative to mean terminal wealth. EaR depends explicitly on the adopted investment strategy \(\pi\) and provides a tradeoff between investing in the portfolio with position \(\pi\) and its expected shortfall as a result of adopting such investment strategy. The authors obtained closed-form expressions for the best constantly-rebalanced portfolio investment strategy and the efficient frontier of the mean-EaR problem. The mean-EaR analysis is compared to the classical mean-variance analysis and to the mean-capital-at-risk analysis. For the mean-variance efficient frontier, the variance is always a convex function of the expected terminal wealth, thus the marginal risk is increasing, while the marginal risk measured by EaR can be decreasing at least on an infinite part of the mean-EaR frontier. In a numerical example it is illustrated an increasing and concave mean-EaR efficient frontier.
scientific article; zbMATH DE number 5346081