# 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… Expand

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#### References

SHOWING 1-10 OF 79 REFERENCES

Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix

- Mathematics, Economics
- 2016

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… Expand

Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities

- Mathematics
- 2014

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… Expand

Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach

- Economics
- 2004

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,… Expand

Model Misspecification and Under-Diversification

- Economics
- 2001

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… Expand

Tractable Robust Expected Utility and Risk Models for Portfolio Optimization

- Economics
- 2009

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… Expand

Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization

- Economics, Computer Science
- Manag. Sci.
- 2008

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. Expand

Robust Portfolio Control with Stochastic Factor Dynamics

- Computer Science
- Oper. Res.
- 2013

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. Expand

Keynes Meets Markowitz: The Trade-Off between Familiarity and Diversification

- Economics, Computer Science
- Manag. Sci.
- 2012

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. Expand

Good deal hedging and valuation under combined uncertainty about drift and volatility

- Mathematics, Economics
- 2017

We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral… Expand

Optimal investments for risk- and ambiguity-averse preferences: a duality approach

- Economics, Computer Science
- Finance Stochastics
- 2007

This paper studies the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer. Expand