Mean-Variance Adjusting Model for Portfolio Selection Problem with Fuzzy Random Returns

2014 ◽  
Author(s):  
Zhongfeng Qin ◽  
Lei Xu
Keyword(s):  
Portfolio Selection ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
Mean Variance ◽  
Fuzzy Random

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

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.

scholarly journals ON TIME CONSISTENCY FOR MEAN-VARIANCE PORTFOLIO SELECTION

2020 ◽  
Vol 23 (06) ◽  
pp. 2050042 ◽  
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.

The general mean-variance portfolio selection problem

1994 ◽  
Vol 347 (1684) ◽  
pp. 543-549 ◽  
Keyword(s):  
Portfolio Selection ◽  
Portfolio Analysis ◽  
Selection Problem ◽  
Analysis Problem ◽  
Portfolio Selection Problem ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper states the ‘general mean-variance portfolio analysis problem’ and its solution, and briefly discusses its use in practice.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
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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