Since Markowitz published his seminal work on mean-variance portfolio selection in 1952, almost all literature in the past half century adhere their investigation to a binding budget spending assumption on this classical investment issue. In the mean-variance world for a market of all risky...

The bounds for risk measures of a portfolio when its components have known marginal distributions but the dependence among the risks is unknown are often too wide to be useful in practice. Moreover, availability of additional dependence information, such as knowledge of some higher-order...

Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an...

In the existing literature, the value-at-risk (VaR) is one of the most representative downside risk measures due to its wide spectra of applications in practice. In this paper, we investigate the dynamic mean-VaR portfolio selection formulation, while the state-of-the-art has only witnessed...

We first study mean-variance efficient portfolios when there are no trading constraints and show that optimal strategies perform poorly in bear markets. We then assume investors use a stochastic benchmark (linked to the market) as a reference portfolio. We derive mean-variance efficient...

In standard portfolio theories such as Mean-Variance optimization, Expected Utility Theory, Rank Dependent Utility Theory, Yaari's Dual Theory and Cumulative Prospect Theory, the worst outcomes for optimal strategies occur when the market declines (e.g, during crises), which is at odds with the...

An investor does not always invest in risky assets in all time periods, often due to the management fee charged for hiring an agent in managing his investment in risky assets. Motivated by this observed common phenomenon, this paper considers the time cardinality constrained mean-variance...

We consider in this paper the mean-variance formulation in multi-period portfolio selection under no-shorting constraint. Recognizing the structure of a piecewise quadratic value function, we prove that the optimal portfolio policy is piecewise linear with respect to the current wealth level,...

Recent literature deals with bounds on the Value-at-Risk (VaR) of risky portfolios when only the marginal distributions of the components are known. In this paper we study Value-at-Risk bounds when the variance of the portfolio sum is also known, a situation that is of considerable interest in...

Different risk measures emphasize different aspects of a random loss. If we examine the investment performance according to different spectra of the risk measures, any policy generated from a mean-risk portfolio model with a sole risk measure may not be a good choice. We study in this paper the...