C onservationists must make hard choices about where to invest limited resources for the protection of biological diversity. Numerous prioritization schemes have identified places where biodiversity is especially rich or risks are especially urgent (1). Application of return on investment (ROI) thinking promises to make conservation investments much more efficient by explicitly incorporating ec...

Over sixty years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an over...

short-selling prohibition has been one of the primary assumptions of markowitz mean-variance model. solving markowitz quadratic model creates investment efficient frontier by considering only two return and budget constraints. in order to develop a more realistic portfolio selection model, in this paper, a new mathematical model is developed to allow short-selling under some practical constrain...

Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two-period conic portfolio problem is formulated and implemented. This development leads to a mean ask price frontier, where the latter employs concave distortions. The modeling permits access to skewness...

In this paper we consider the problem of "nding the e$cient frontier associated with the standard mean}variance portfolio optimisation model. We extend the standard model to include cardinality constraints that limit a portfolio to have a speci"ed number of assets, and to impose limits on the proportion of the portfolio held in a given asset (if any of the asset is held). We illustrate the di!e...

To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks w...

Mathematical programming methods dominate in the portfolio optimization problems, but they cannot be used if we introduce a constraint limiting the number of different assets included in the portfolio. To solve this model some of the heuristics methods (such as genetic algorithm, neural networks and particle swarm optimization algorithm) must be used. In this paper we utilize binary particle sw...

the markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. considering real world limits and conditions, the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. therefore, the use of meta-heuristic methods such as neural networks and evolutionar...

The effective (geometric mean) return of a periodically rebalanced portfolio always exceeds the weighted sum of the component geometric means. Some approximate formulae for estimating this effective return are derived and tested. One special case of these formulae is shown to be particularly simple, and is used to provide easily computed estimates of the benefits of diversification and rebalanc...

In Brennan and Lo (2010), a mean-variance efficient frontier is defined as “impossible” if every portfolio on that frontier has negative weights, which is incompatible with the Capital Asset Pricing Model (CAPM) requirement that the market portfolio is mean-variance efficient. We prove that as the number of assets n grows, the probability that a randomly chosen frontier is impossible tends to o...