HYPER SENSITIVITY ANALYSIS OF PORTFOLIO OPTIMIZATION PROBLEMS

Hyper Sensitivity Analysis (HSA) is an intuitive generalization of conventional sensitivity analysis, where the term "hyper" indicates that the sensitivity analysis is conducted with respect to functions rather than numeric values. In this paper Composite Concave Programming is used to perform HSA in the area of Portfolio Optimization Problems. The concept of HSA is suited for situations where several candidates for the function quantifying the utility of (mean, variance) pairs are available. We discuss the applications of HSA to two types of mean–variance portfolio optimization problems: the classical one and a discrete knapsack-type portfolio selection problem. It is explained why in both cases the methodology can be applied to full size problems.

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Time-Consistent Strategies for a Multiperiod Mean-Variance Portfolio Selection Problem

Journal of Applied Mathematics ◽

10.1155/2013/841627 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 12

Author(s):

Huiling Wu

Keyword(s):

Nash Equilibrium ◽

Portfolio Selection ◽

Optimization Problems ◽

Selection Problem ◽

Equilibrium Strategy ◽

Nash Equilibrium Strategy ◽

Portfolio Selection Problem ◽

Nash Equilibrium Strategies ◽

Mean Variance Portfolio ◽

Mean Variance

It remained prevalent in the past years to obtain the precommitment strategies for Markowitz's mean-variance portfolio optimization problems, but not much is known about their time-consistent strategies. This paper takes a step to investigate the time-consistent Nash equilibrium strategies for a multiperiod mean-variance portfolio selection problem. Under the assumption that the risk aversion is, respectively, a constant and a function of current wealth level, we obtain the explicit expressions for the time-consistent Nash equilibrium strategy and the equilibrium value function. Many interesting properties of the time-consistent results are identified through numerical sensitivity analysis and by comparing them with the classical pre-commitment solutions.

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Bicriteria Exploratory Mean-Variance Portfolio Selection Problem in Continuous Time

10.1109/ccdc52312.2021.9602795 ◽

2021 ◽

Author(s):

Heng Zhang

Keyword(s):

Portfolio Selection ◽

Continuous Time ◽

Selection Problem ◽

Portfolio Selection Problem ◽

Mean Variance Portfolio ◽

Mean Variance

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A Two-level Reinforcement Learning Algorithm for Ambiguous Mean-variance Portfolio Selection Problem

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/624 ◽

2020 ◽

Author(s):

Xin Huang ◽

Duan Li

Keyword(s):

Reinforcement Learning ◽

Portfolio Selection ◽

Current Knowledge ◽

Lower Layer ◽

Experimental Studies ◽

Selection Problem ◽

Multiple Time ◽

Portfolio Selection Problem ◽

Mean Variance Portfolio ◽

Mean Variance

Traditional modeling on the mean-variance portfolio selection often assumes a full knowledge on statistics of assets' returns. It is, however, not always the case in real financial markets. This paper deals with an ambiguous mean-variance portfolio selection problem with a mixture model on the returns of risky assets, where the proportions of different component distributions are assumed to be unknown to the investor, but being constants (in any time instant). Taking into consideration the updates of proportions from future observations is essential to find an optimal policy with active learning feature, but makes the problem intractable when we adopt the classical methods. Using reinforcement learning, we derive an investment policy with a learning feature in a two-level framework. In the lower level, the time-decomposed approach (dynamic programming) is adopted to solve a family of scenario subcases where in each case the series of component distributions along multiple time periods is specified. At the upper level, a scenario-decomposed approach (progressive hedging algorithm) is applied in order to iteratively aggregate the scenario solutions from the lower layer based on the current knowledge on proportions, and this two-level solution framework is repeated in a manner of rolling horizon. We carry out experimental studies to illustrate the execution of our policy scheme.

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ON TIME CONSISTENCY FOR MEAN-VARIANCE PORTFOLIO SELECTION

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500429 ◽

2020 ◽

Vol 23 (06) ◽

pp. 2050042 ◽

Cited By ~ 1

Author(s):

ELENA VIGNA

Keyword(s):

Portfolio Selection ◽

Optimal Strategy ◽

Time Consistency ◽

Time Inconsistency ◽

Selection Problem ◽

Portfolio Selection Problem ◽

The Mean ◽

Optimal Approach ◽

Mean Variance Portfolio ◽

Mean Variance

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare three common approaches to time inconsistency for the mean-variance portfolio selection problem over [Formula: see text]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point [Formula: see text] and is dominated by the dynamically optimal strategy from [Formula: see text] onwards. Existence and uniqueness of the break even point [Formula: see text] is proven.

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An Entropy-Based Approach to Portfolio Optimization

Entropy ◽

10.3390/e22030332 ◽

2020 ◽

Vol 22 (3) ◽

pp. 332 ◽

Cited By ~ 4

Author(s):

Peter Joseph Mercurio ◽

Yuehua Wu ◽

Hong Xie

Keyword(s):

Objective Function ◽

Portfolio Optimization ◽

Historical Data ◽

Optimization Problems ◽

Improved Method ◽

Financial Industry ◽

New Family ◽

The Mean ◽

Mean Variance Portfolio ◽

Mean Variance

This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

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