Portfolio diversification and model uncertainty: A robust dynamic mean‐variance approach

@article{Pham2021PortfolioDA,
  title={Portfolio diversification and model uncertainty: A robust dynamic mean‐variance approach},
  author={Huy{\^e}n Pham and Xiaoli Wei and Chao Zhou},
  journal={Mathematical Finance},
  year={2021}
}
This paper is concerned with a multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the effects on portfolio diversification. We prove a separation principle for the associated robust control problem, which allows to reduce the determination of the optimal dynamic strategy to the parametric computation… 
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References

SHOWING 1-10 OF 79 REFERENCES
Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix
This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated
Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities
In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
In this paper, we show how an investor can incorporate uncertainty about expected returns when choosing a mean-variance optimal portfolio. In contrast to the Bayesian approach to estimation error,
Model Misspecification and Under-Diversification
In this Paper we develop a model of intertemporal portfolio choice where an investor accounts explicitly for the possibility of model misspecification. This work is motivated by the difficulty in
Correlation Ambiguity and Under-Diversification
We study effects of correlation ambiguity on portfolio choice when the number of risky assets is large. We find that the optimal portfolio contains only a fraction of available risky assets. With 100
Tractable Robust Expected Utility and Risk Models for Portfolio Optimization
Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of
Correlation Uncertainty , Heterogeneous Beliefs and Asset Prices
We construct an equilibrium model in the presence of correlation uncertainty and heterogeneous ambiguity-averse investors. In this model the level of correlation uncertainty and asset characteristic
Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization
TLDR
The proposed method results in the optimization of a modified VaR measure, Asymmetry-Robust VaR (ARVaR), that takes into consideration asymmetries in the distributions of returns and is coherent, which makes it desirable from a financial theory perspective.
Robust Portfolio Control with Stochastic Factor Dynamics
TLDR
By acknowledging uncertainty in the estimated model, the robust rules lead to less aggressive trading and are less sensitive to sharp moves in underlying prices.
Keynes Meets Markowitz: The Trade-Off between Familiarity and Diversification
TLDR
The concepts of ambiguity and ambiguity aversion are used to formalize the idea of an investor's “familiarity” toward assets and show that for any given level of expected returns, the optimal portfolio depends on two quantities.
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