scholarly journals Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

2021 ◽  
Author(s):  
Jose Blanchet ◽  
Lin Chen ◽  
Xun Yu Zhou
Keyword(s):  
Portfolio Selection ◽  
Wasserstein Distance ◽  
Empirical Measure ◽  
Back Testing ◽  
Robust Version ◽  
Distributionally Robust ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance ◽  
Wasserstein Distances

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

scholarly journals A Mean-Variance Portfolio Selection Model with Interval-Valued Possibility Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yunyun Sui ◽  
Jiangshan Hu ◽  
Fang Ma
Keyword(s):  
Portfolio Selection ◽  
Return Rate ◽  
Selection Model ◽  
Expected Return ◽  
Interval Numbers ◽  
Numerical Example ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance ◽  
Interval Valued

In recent years, fuzzy set theory and possibility theory have been widely used to deal with an uncertain decision environment characterized by vagueness and ambiguity in the financial market. Considering that the expected return rate of investors may not be a fixed real number but can be an interval number, this paper establishes an interval-valued possibilistic mean-variance portfolio selection model. In this model, the return rate of assets is regarded as a fuzzy number, and the expected return rate of assets is measured by the interval-valued possibilistic mean of fuzzy numbers. Therefore, the possibilistic portfolio selection model is transformed into an interval-valued optimization model. The optimal solution of the model is obtained by using the order relations of interval numbers. Finally, a numerical example is given. Through the numerical example, it is shown that, when compared with the traditional possibilistic model, the proposed model has more constraints and can better reflect investor psychology. It is an extension of the traditional possibilistic model and offers greater flexibility in reflecting investor expectations.

SOME FURTHER ANALYTICAL PROPERTIES OF THE CONSTANT CORRELATION MODEL FOR PORTFOLIO SELECTION

2006 ◽  
Vol 09 (07) ◽  
pp. 1071-1091 ◽  
Author(s):  
CLARENCE C. Y. KWAN
Keyword(s):  
Portfolio Selection ◽  
Correlation Matrix ◽  
Correlation Model ◽  
Simple Alternative ◽  
Computational Advantage ◽  
Analytical Properties ◽  
Important Input ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance

The constant correlation model is a mean-variance portfolio selection model where, for a given set of risky securities, the correlation of returns between any pair of different securities is considered to be the same. Support for the model is from previous empirical evidence that sample averages of correlations outperform various more sophisticated models in forecasting the correlation matrix, an important input component for portfolio analysis. To enable a better understanding of the constant correlation model, this study identifies some additional analytical properties of the model and relates them to familiar portfolio concepts. By comparing computational times for portfolio construction with and without simplifying the correlation matrix in a simulation study, this study also confirms the model's computational advantage. This study is intended to provide further analytical support for the model as a viable, simple alternative to those portfolio selection models where input requirements and the attendant computations are more burdensome.

scholarly journals Portfolio Selection with Jumps under Regime Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Lin Zhao
Keyword(s):  
Markov Chain ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Regime Switching ◽  
Jump Processes ◽  
Bank Account ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance

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 and multiple 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 employed to model the problem.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

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