Academics and practitioners optimize portfolios using the mean-variance approach far more often than the meansemivariance approach, despite the fact that semivariance is often considered a more plausible measure of risk than variance. The popularity of the mean-variance approach follows in part from the fact that mean-variance problems have well-known closed-form solutions, whereas meansemivari...

The Markowitz model for single period portfolio optimization quantifies the problem by means of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe’s work on linear approximation to th...

An insurance model, with realistic assumptions about coverage, deductible and premium, is studied. Insurance is shown to decrease the variance of the cost to the insured, but increase the expected cost, a tradeoff that places our model in the Markowitz mean–variance model.

We study rankings of completely and partially diversified portfolios and also of specialized assets when investors follow so-called Markowitz preferences. It turns out that diversification strategies for Markowitz investors are more complex than in the case of risk-averse and risk-inclined investors, whose investment strategies have been extensively investigated in the literature. In particular...

Following the seminal work by Markowitz, the portfolio selection problem is usually modeled as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model, the risk is measured with variance. Several other risk measures have been later considered thus creating the entire family of mean-risk (Markowitz type) ...