A Dynamic Mean-Variance Analysis for Log Returns

Dai, Min; Jin, Hanqing; Kou, Steven; Xu, Yuhong

doi:10.1287/mnsc.2019.3493

Cited by 68 publications

(52 citation statements)

References 47 publications

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“…Very recently, Mu et al [27] study a portfolio selection problem with both wealth-dependent risk aversion and wealth-dependent skewness preference and obtain the equilibrium investment strategy in semi-closed form. More related studies can also be found in [9,10,17,19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

Kang¹,

Huang²,

Hu³

et al. 2022

Preprint

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This paper considers a robust time-consistent mean-variance-skewness portfolio selection problem for an ambiguity-averse investor by taking into account wealth-dependent risk aversion and wealth-dependent skewness preference as well as model uncertainty. The robust equilibrium investment strategy and corresponding equilibrium value function are characterized for such a problem by employing an extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) system via a game theoretic approach. Furthermore, the robust equilibrium investment strategy and corresponding equilibrium value function are obtained in semi-closed form for a special robust time-consistent mean-variance-skewness portfolio selection problem. Finally, some numerical experiments are provided to indicate several new findings concerned with the robust equilibrium investment strategy and the utility losses.

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Section: Introductionmentioning

confidence: 99%

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

Kang¹,

Huang²,

Hu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In the incomplete markets with stochastic volatility, [28] considered the open-loop control framework for time-consistent mean-variance portfolio problems. A dynamic mean-variance analysis for log returns within the game-theoretic approach was proposed in [10]. Further, [13] introduced a "dynamic utility" under which the original time-inconsistent problem became a time-consistent one, and investigated possible approaches to study a general time-inconsistent optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Multi-time state mean-variance model in continuous time

Yang

2021

ESAIM: COCV

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The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

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“…There also have numerous extensions of the mean-risk portfolio optimization from the single-period setting to the dynamic, continuous-time one (e.g. Zhou and Li, 2000;Bielecki et al, 2005;Jin et al, 2005;Basak and Chabakauri, 2010;He et al, 2015;Zhou et al, 2017;Gao et al, 2017;Dai et al, 2021;He and Jiang, 2021). In particular, He et al (2015) study a continuous-time mean-risk portfolio choice when risk is measured by the weighted Valueat-Risk (WVaR) but their results are rather pessimistic.…”

Section: Introductionmentioning

confidence: 99%

“…Alexander and Baptista, 2002Jin et al, 2006;Adam et al, 2008). However, there is a discrepancy between single-period and dynamic portfolio choice models, as the latter typically considers mean-risk criterion for terminal wealth; an exception is Dai et al (2021) who study continuous-time mean-variance portfolio choice for portfolio log-returns. We similarly adopt the mean-WVaR criterion for log-returns which naturally generalize the single-period return when returns are continuously compounded.…”

Section: Introductionmentioning

confidence: 99%

Dynamic growth-optimum portfolio choice under risk control

Wei¹,

Xu²

2021

Preprint

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This paper studies a mean-risk portfolio choice problem for log-returns in a continuoustime, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth up to the concave envelope of a certain function, and obtain analytical expressions for the optimal wealth and portfolio policy when the risk is measured by VaR or ES. In addition, we find that the efficient frontier is a concave curve that connects the minimumrisk portfolio with the growth optimal portfolio, as opposed to the vertical line when WVaR is used on terminal wealth. Our results advocate the use of mean-WVaR criterion for logreturns instead of terminal wealth in dynamic portfolio choice.

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A Dynamic Mean-Variance Analysis for Log Returns

Cited by 68 publications

References 47 publications

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

Robust equilibrium strategy for mean-variance-skewness portfolio selection problem

Multi-time state mean-variance model in continuous time

Dynamic growth-optimum portfolio choice under risk control

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