In this tutorial paper we introduce different approaches to Markowitz portfolio optimization, and we show how to solve such problems in MATLAB, R and Python using the MOSEK optimization toolbox for MATLAB, the Rmosek package, and the MOSEK Python API, respectively. We first consider conic formulations of the basic portfolio selection problem, and we then discuss more advanced models for transac...

Diversified models for portfolio selection based on uncertain semivariance Lin Chen, Jin Peng, Bo Zhang & Isnaini Rosyida To cite this article: Lin Chen, Jin Peng, Bo Zhang & Isnaini Rosyida (2016): Diversified models for portfolio selection based on uncertain semivariance, International Journal of Systems Science, DOI: 10.1080/00207721.2016.1206985 To link to this article: http://dx.doi.org/10...

This paper proposes the mean-dynamic VaR multi-period portfolio selection model with the transaction costs and the constraints on trade volumes. The Bat algorithm is applied to solve the multi-period mean-dynamic VaR model. Numerical results show that the Bat algorithm is effective and feasible to solve multi-period portfolio selection problems.

We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account andmultiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is ...

‘Separable’ uncertainty sets have been widely used in robust portfolio selection models (e.g. see [E. Erdoğan, D. Goldfarb, and G. Iyengar, Robust portfolio management, manuscript, Department of Industrial Engineering and Operations Research, Columbia University, New York, 2004; D. Goldfarb and G. Iyengar, Robust portfolio selection problems, Math. Oper. Res. 28 (2003), pp. 1–38; R.H. Tütüncü a...

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...

Robust portfolio modeling (RPM) [Liesiö, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488–1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplet...

A major challenge for stochastic optimization is the cost of updating model parameters especially when the number of parameters is large. Updating parameters frequently can prove to be computationally or monetarily expensive. In this paper, we introduce an efficient primal-dual based online algorithm that performs lazy updates to the parameter vector and show that its performance is competitive...

Robust portfolio modeling (RPM) [Liesiö, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488–1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplet...

We study asset allocation when the conditional moments of returns are partly predictable. Rather than first model the return distribution and subsequently characterize the portfolio choice, we determine directly the dependence of the optimal portfolio weights on the predictive variables. We combine the predictors into a single index that best captures time variations in investment opportunities...