scholarly journals Constrained Dynamic Mean-Variance Portfolio Selection in Continuous-Time

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 252
Author(s):  
Weiping Wu ◽  
Lifen Wu ◽  
Ruobing Xue ◽  
Shan Pang
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Value Function ◽  
Optimal Solution ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
Cone Constraints ◽  
Lq Optimal Control ◽  
Mean Variance Portfolio ◽  
Portfolio Policy

This paper revisits the dynamic MV portfolio selection problem with cone constraints in continuous-time. We first reformulate our constrained MV portfolio selection model into a special constrained LQ optimal control model and develop the optimal portfolio policy of our model. In addition, we provide an alternative method to resolve this dynamic MV portfolio selection problem with cone constraints. More specifically, instead of solving the correspondent HJB equation directly, we develop the optimal solution for this problem by using the special properties of value function induced from its model structure, such as the monotonicity and convexity of value function. Finally, we provide an example to illustrate how to use our solution in real application. The illustrative example demonstrates that our dynamic MV portfolio policy dominates the static MV portfolio policy.

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.

scholarly journals Two-Stage Fuzzy Portfolio Selection Problem with Transaction Costs

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yanju Chen ◽  
Ye Wang
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Optimal Solution ◽  
Single Stage ◽  
Selection Problem ◽  
Stage Model ◽  
Two Stage ◽  
Portfolio Selection Problem ◽  
Fuzzy Portfolio Selection ◽  
Proposed Model

This paper studies a two-period portfolio selection problem. The problem is formulated as a two-stage fuzzy portfolio selection model with transaction costs, in which the future returns of risky security are characterized by possibility distributions. The objective of the proposed model is to achieve the maximum utility in terms of the expected value and variance of the final wealth. Given the first-stage decision vector and a realization of fuzzy return, the optimal value expression of the second-stage programming problem is derived. As a result, the proposed two-stage model is equivalent to a single-stage model, and the analytical optimal solution of the two-stage model is obtained, which helps us to discuss the properties of the optimal solution. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness. The computational results provided by the proposed model show that the more risk-averse investor will invest more wealth in the risk-free security. They also show that the optimal invested amount in risky security increases as the risk-free return decreases and the optimal utility increases as the risk-free return increases, whereas the optimal utility increases as the transaction costs decrease. In most instances the utilities provided by the proposed two-stage model are larger than those provided by the single-stage model.

scholarly journals Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming

2016 ◽  
Vol 6 (2) ◽  
pp. 121-128 ◽  
Author(s):  
Fusun Kucukbay ◽  
Ceyhun Araz
Keyword(s):  
Portfolio Selection ◽  
Goal Programming ◽  
Optimal Solution ◽  
Good Alternative ◽  
Fuzzy Goal Programming ◽  
Selection Problem ◽  
Physical Programming ◽  
Portfolio Selection Problem ◽  
Linear Physical Programming ◽  
Fuzzy Goal

Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP) technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP). Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

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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