scholarly journals Mean–Variance Portfolio Management with Functional Optimization

2021 ◽  
pp. 2050055
Author(s):  
Ka Wai Tsang ◽  
Zhaoyi He
Keyword(s):  
Portfolio Management ◽  
Optimization Problems ◽  
Empirical Studies ◽  
Optimal Solution ◽  
Weight Vector ◽  
Optimization Approach ◽  
Functional Optimization ◽  
Mean And Variance ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean–variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.

scholarly journals Applying Least Squares Support Vector Machines to Mean-Variance Portfolio Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Wang ◽  
Junseok Kim
Keyword(s):  
Support Vector Machines ◽  
Least Squares ◽  
Portfolio Management ◽  
Stock Exchange ◽  
Efficient Frontier ◽  
Support Vector ◽  
Research Fields ◽  
Vector Machines ◽  
Mean Variance Portfolio ◽  
Mean Variance

Portfolio selection problem introduced by Markowitz has been one of the most important research fields in modern finance. In this paper, we propose a model (least squares support vector machines (LSSVM)-mean-variance) for the portfolio management based on LSSVM. To verify the reliability of LSSVM-mean-variance model, we conduct an empirical research and design an algorithm to illustrate the performance of the model by using the historical data from Shanghai stock exchange. The numerical results show that the proposed model is useful when compared with the traditional Markowitz model. Comparing the efficient frontier and total wealth of both models, our model can provide a more measurable standard of judgment when investors do their investment.

scholarly journals An Entropy-Based Approach to Portfolio Optimization

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 332 ◽  
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.

scholarly journals A remark on some extensions of the mean-variance portfolio selection models

2021 ◽  
Vol 16 (3) ◽  
pp. 26-34
Author(s):  
Enrico Moretto ◽  
Keyword(s):  
Portfolio Management ◽  
Proper Time ◽  
Research Question ◽  
The Third ◽  
Management Techniques ◽  
The Common ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
The Right ◽  
Mean Variance

Quantitative risk management techniques should prove their efficacy when financially turbulent periods are about to occur. Along the common saying “who needs an umbrella on a sunny day?”, a theoretical model is really helpful when it carries the right suggestion at the proper time, that is when markets start behaving hecticly. The beginning of the third decade of the 21st century carried along a turmoil that severely affected worldwide economy and changed it, probably for good. A consequent and plausible research question could be this: which financial quantitative approaches can still be considered reliable? This article tries to partially answer this question by testing if the mean-variance selection model (Markowitz [16], [17]) and some of his refinements can provide some useful hints in terms of portfolio management.

Exploring the mean-variance portfolio optimization approach for planning wind repowering actions in Spain

2017 ◽  
Vol 106 ◽  
pp. 335-342 ◽  
Author(s):  
F.J. Santos-Alamillos ◽  
N.S. Thomaidis ◽  
J. Usaola-García ◽  
J.A. Ruiz-Arias ◽  
D. Pozo-Vázquez
Keyword(s):  
Portfolio Optimization ◽  
Optimization Approach ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

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.

HYPER SENSITIVITY ANALYSIS OF PORTFOLIO OPTIMIZATION PROBLEMS

2004 ◽  
Vol 21 (03) ◽  
pp. 297-317 ◽  
Author(s):  
LEONID CHURILOV ◽  
IMMANUEL M. BOMZE ◽  
MOSHE SNIEDOVICH ◽  
DANIEL RALPH
Keyword(s):  
Sensitivity Analysis ◽  
Portfolio Optimization ◽  
Portfolio Selection ◽  
Optimization Problems ◽  
Selection Problem ◽  
Full Size ◽  
Concave Programming ◽  
Hyper Sensitivity ◽  
Mean Variance Portfolio ◽  
Mean Variance

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.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

DYNAMIC MEAN–VARIANCE OPTIMIZATION PROBLEMS WITH DETERMINISTIC INFORMATION

2018 ◽  
Vol 21 (02) ◽  
pp. 1850011
Author(s):  
MARTIN SCHWEIZER ◽  
DANIJEL ZIVOI ◽  
MARIO ŠIKIĆ
Keyword(s):  
Affine Transformation ◽  
Optimization Problems ◽  
Trading Strategies ◽  
Price Process ◽  
Black Scholes ◽  
Integrable Martingale ◽  
Exponential Lévy Models ◽  
Information Filtration ◽  
Mean Variance Portfolio ◽  
Mean Variance

We solve the problems of mean–variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process [Formula: see text] is a semimartingale, but not adapted to the filtration [Formula: see text] which models the information available for constructing trading strategies. We choose as [Formula: see text] the zero-information filtration and assume that [Formula: see text] is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black–Scholes models.

Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

2021 ◽  
Author(s):  
Frank Schuhmacher ◽  
Hendrik Kohrs ◽  
Benjamin R. Auer
Keyword(s):  
Empirical Evidence ◽  
Sufficient Conditions ◽  
Asset Returns ◽  
Common Belief ◽  
Risky Assets ◽  
Common Stocks ◽  
Elliptical Model ◽  
Mean And Variance ◽  
Mean Variance Portfolio ◽  
Mean Variance

We show that, in the presence of a risk-free asset, the return distribution of every portfolio is determined by its mean and variance if and only if asset returns follow a specific skew-elliptical distribution. Thus, contrary to common belief among academics and practitioners, skewed returns do not allow a rejection of mean-variance analysis. Our work differs from Chamberlain's [Chamberlain G (1983) A characterization of the distributions that imply mean-variance utility functions. J. Econom. Theory 29(1):185–201.] by focusing on the returns of portfolios, where the weights over the risk-free asset and the risky assets sum to unity. Furthermore, it extends Meyer's [Meyer J, Rasche RH (1992) Sufficient conditions for expected utility to imply mean-standard deviation rankings: Empirical evidence concerning the location and scale condition. Econom. J. (London) 102(410):91–106.] by introducing elliptical noise into their generalized location-scale framework. To emphasize the relevance of our skew-elliptical model, we additionally provide empirical evidence that it cannot be rejected for the returns of typical portfolios of common stocks or popular alternative investments. This paper was accepted by Kay Giesecke, finance.

A microbial kinetic optimization approach

2021 ◽  
pp. 1-17
Author(s):  
Xiong Ding ◽  
Yan Lu
Keyword(s):  
Culture System ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Culture Fluid ◽  
Microbial Populations ◽  
Optimization Approach ◽  
Toxic Substances ◽  
Global Optimal ◽  
Growth Changes ◽  
The Impact

In order to solve some optimization problems with many local optimal solutions, a microbial dynamic optimization (MDO) algorithm is proposed by the kinetic theory of hybrid food chain microorganism cultivation with time delay. In this algorithm, it is assumed that multiple microbial populations are cultivated in a culture system. The growth of microbial populations is not only affected by the flow of culture fluid injected into the culture system, the concentration of nutrients and harmful substances, but also by the interaction between the populations. The influence of culture medium which is injected regularly will suddenly increase the concentration of nutrients and toxic substances, it will suddenly increase the impact on the population. These characteristics are used to construct absorption operators, grabbing operators, hybrid operators, and toxin operators; the global optimal solution of the optimization problem can be quickly solved by these operators and the population growth changes. The simulation experiment results show that the MDO algorithm has certain advantages for solving optimization problems with higher dimensions.

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