Robust mean variance optimization problem under Rényi divergence information

Ding, Ke-wei; Chen, Zhang-you; Huang, Nan-jing

doi:10.1080/02331934.2017.1394298

Cited by 8 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As Ding et al (2018) argued, the Kullback-Leibler (KL) divergence used in Calafiore ( 2007) is a special case of Rényi divergence with order one, hence they used it in a more general DRO formulation of the mean-variance PSP. They assumed that there is ambiguity about the true distribution of returns, and constructed an ambiguity set that contains all distributions within a certain distance, measured using Rényi divergence, from the empirical distribution.…”

Section: Distributionally Robust Mean-variancementioning

confidence: 99%

“…Their model was solved in three cases where; only the mean return vector is uncertain, only the covariance matrix is uncertain, and both are uncertain. It is worth mentioning that even though the ambiguity set used in Ding et al (2018) is more general than the KL-divergence, their formulations are special cases from the distribution function perspective since both the empirical and the true distribution function of the asset returns are assumed to be multivariate normal.…”

Section: Distributionally Robust Mean-variancementioning

confidence: 99%

See 1 more Smart Citation

Robust Portfolio Selection Problems: A Comprehensive Review

Ghahtarani¹,

Ahmed²,

Ghasemi³

2021

Preprint

View full text Add to dashboard Cite

In this paper, we provide a comprehensive review of recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives. A multi-dimensional classification of the models and methods proposed in the literature is presented, based on the types of financial problems, uncertainty sets, robust optimization approaches, and mathematical formulations. Several open questions and potential future research directions are identified.

show abstract

Section: Distributionally Robust Mean-variancementioning

confidence: 99%

Section: Distributionally Robust Mean-variancementioning

confidence: 99%

Robust Portfolio Selection Problems: A Comprehensive Review

Ghahtarani¹,

Ahmed²,

Ghasemi³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…where b is a known vector, representing a priori expected rates of return, and δ > 0 represents a level of ambiguity around b due to estimation error. It is known from Lemma 2.2 in [10] that Θ is a convex set. This ellipsoidal set in which varies the uncertain drift, for fixed correlation, is used in [2], and allows to take into account the correlation structure of the assets in the drift uncertainty modelling.…”

Section: Model Uncertainty Settingmentioning

confidence: 99%

Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach

Pham¹,

Wei²,

Zhou³

2018

Preprint

View full text Add to dashboard Cite

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 of the minimal risk premium function. Our results provide a justification for underdiversification, as documented in empirical studies. We explicitly quantify the degree of under-diversification in terms of correlation and Sharpe ratio ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. This extends to the continuous-time setting the results obtained by Garlappi, Uppal and Wang [13], and Liu and Zeng [24] in a one-period model.

show abstract

“…Robust utility maximization in the optimal investment problems has been widely investigated under different situations with different approaches, among others, a stochastic control method in [10,26], a stochastic differential game approach in [48], a duality method in [49]. For more details on various portfolio selection problems, we refer to [1,14,20,21,27,53,54] and the references therein. In particular, we refer to [30,31,32] for the review of the recent advancements in robust investment management.…”

Section: Introductionmentioning

confidence: 99%

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Li¹,

Li²,

Liang³

2021

SIAM J. Finan. Math.

View full text Add to dashboard Cite

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.

show abstract

Robust mean variance optimization problem under Rényi divergence information

Cited by 8 publications

References 27 publications

Robust Portfolio Selection Problems: A Comprehensive Review

Robust Portfolio Selection Problems: A Comprehensive Review

Portfolio diversification and model uncertainty: a robust dynamic mean-variance approach

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Contact Info

Product

Resources

About