The problem of interest in this paper is the optimization of portfolios of real and contractual assets, including derivative instruments, subject to a Value-at-Risk (VaR) constraint. The focus in this paper is on translating VaR definitions for one period of time, say a year, to decisions on shorter periods of time, say a week or a month. Thus, if a VaR constraint is imposed on annual cash flow...

Our objective is to develop a methodology to detect regions in risk-return space where the out-of-sample performance of portfolios is consistent with their in-sample performance. We use the Berkowitz statistic to evaluate the accuracy of the density forecast, derived from in-sample portfolio returns, of out-of-sample portfolio returns. Defined by its coordinates in risk-return space, a portfoli...

Value at risk (VaR) is an important and widely used measure of the extent to which a given portfolio is subject to risk present in nancial markets. Considerable amount of research was dedicated during recent years to development of acceptable methods for evaluation of this risk measure. In this paper, we present a method of calculating the portfolio which gives the optimal VaR among those, whic...

The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification measure and the real world constraints imposed to the model make the problem difficult to be solved with exact methods. Thanks to the exploratory mechanism, n-MOEA concentrates the sea...

We investigate a continuous-time mean–variance portfolio selection problem. Different from the general stochastic dynamic programming approach, such as using Hamilton–Jacobi–Bellman (HJB) equation, this paper adopts the Lagrange duality method and the finite difference approach to derive explicit closed-form expressions for the efficient investment strategy and the mean–variance efficient front...

The mean-variance framework for portfolio selection should be revised when investor’s concern is the downside risk. This is especially true when the asset returns are not normal. In this paper, we incorporate value-at-risk (VaR) in portfolio selection and the mean-VaR framework is proposed. Due to the twoobjective optimization problem faced by the meanVaR framework, an evolutionary multi-object...

We investigate an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems and thus can be solved quickly for problems of large scale. We compare its performance to that of m...

This paper quantifies the diversification potential of timberland investments in a meanvariance framework. The starting point is a broad set of benchmark assets represented by various indexes. Including publicly traded timberland investments in the portfolio does not significantly increase meanvariance efficiency. At first sight, U.S. private equity timberland seems to improve the mean-variance...

This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We invoke the HJB equation of this problem and give an explicit viscosity solution of the HJB equation. Furthermore, via this explicit viscosity solution, we obta...

In this paper, we propose a discrete-time model for mean-variance portfolio selection. One of the distinct features is that the system under consideration is a Markov modulated system. We show that under suitable conditions and scaling, the process of interest goes to a switching diffusion limit. Related issues on optimal strategies and efficient frontier will also be mentioned.