Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels

2021 ◽  
pp. 108104
Author(s):  
Xiaomin Gong ◽  
Liangyu Min ◽  
Changrui Yu
Keyword(s):  
Portfolio Selection ◽  
Risk Tolerance ◽  
Expected Return ◽  
Dynamic Risk ◽  
Fuzzy Environment ◽  
Return Levels

UNCERTAINTY PORTFOLIO MODEL IN CROSS CURRENCY MARKETS

2010 ◽  
Vol 18 (06) ◽  
pp. 759-777 ◽  
Author(s):  
WEIJUN XU ◽  
WEIDONG XU ◽  
HONGYI LI ◽  
WEIGUO ZHANG
Keyword(s):  
Portfolio Selection ◽  
Asset Allocation ◽  
Efficient Frontier ◽  
Expected Return ◽  
Fuzzy Variables ◽  
Financial Variables ◽  
Fuzzy Environment ◽  
Exchange Risk ◽  
Asset Selection ◽  
Α Level

Owing to the fluctuations in the financial markets, many financial variables such as expected return, volatility, or exchange rate may occur imprecisely. But many portfolio selection models consider precise input of these values. Therefore, this paper studies a multiobjective international asset allocation problem under fuzzy environment. In our portfolio selection model, both of the return risk and the exchange risk are considered. The coefficient matrices in the objectives and constraints and the decision value are considered as fuzzy variables. The calculation of the portfolio and efficient frontier is derived by considering the exchange risk in the fuzzy environment. An empirical study is performed based on a portfolio of six securities denominated in six different currencies, i.e., USD, EUR, JPY, CNY, HKD, and GBP. The α-level closed interval portfolio [Formula: see text] and the fuzzy efficient frontier are obtained with different values of α ∈ (0, 1]. The empirical results indicate that the fuzzy asset selection method is a useful tool for dealing with the imprecise problem in the real world.

scholarly journals Portfolio Selection Based on Distance between Fuzzy Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Weiyi Qian ◽  
Mingqiang Yin
Keyword(s):  
Mathematical Models ◽  
Portfolio Selection ◽  
Expected Value ◽  
Simple Method ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Investment Return ◽  
New Models ◽  
Different Types

This paper researches portfolio selection problem in fuzzy environment. We introduce a new simple method in which the distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Firstly, two new mathematical models are proposed by expressing divergence as distance, investment return as expected value, and risk as variance and semivariance, respectively. Secondly, the crisp forms of the new models are also provided for different types of fuzzy variables. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.

scholarly journals Comparison of Hurricane Return Levels Using Historical and Geological Records

2008 ◽  
Vol 47 (2) ◽  
pp. 368-374 ◽  
Author(s):  
James B. Elsner ◽  
Thomas H. Jagger ◽  
Kam-biu Liu
Keyword(s):  
Return Period ◽  
Sediment Cores ◽  
Historical Record ◽  
Return Level ◽  
Expected Return ◽  
Hurricane Ivan ◽  
The Past ◽  
Return Levels ◽  
Maximum Likelihood Procedure ◽  
Geological Information

Abstract Hurricane return levels estimated using historical and geological information are quantitatively compared for Lake Shelby, Alabama. The minimum return level of overwash events recorded in sediment cores is estimated using a modern analog (Hurricane Ivan of 2004) to be 54 m s−1 (105 kt) for a return period of 318 yr based on 11 events over 3500 yr. The expected return level of rare hurricanes in the observed records (1851–2005) at this location and for this return period is estimated using a parametric statistical model and a maximum likelihood procedure to be 73 m s−1 (141 kt), with a lower bound on the 95% confidence interval of 64 m s−1 (124 kt). Results are not significantly different if data are taken from the shorter 1880–2005 period. Thus, the estimated sensitivity of Lake Shelby to overwash events is consistent with the historical record given the model. In fact, assuming the past is similar to the present, the sensitivity of the site to overwash events as estimated from the model is likely more accurately set at 64 m s−1.

scholarly journals SCALED AND STABLE MEAN-VARIANCE-EVAR PORTFOLIO SELECTION STRATEGY WITH PROPORTIONAL TRANSACTION COSTS

2017 ◽  
Vol 18 (4) ◽  
pp. 561-584 ◽  
Author(s):  
Ebenezer Fiifi Emire ATTA MILLS ◽  
Bo YU ◽  
Jie YU
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Downside Risk ◽  
Estimation Risk ◽  
Expected Return ◽  
Proportional Transaction Costs ◽  
Portfolio Returns ◽  
L2 Norm ◽  
The Mean ◽  
Mean Variance

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

scholarly journals A Scalable Algorithm for Sparse Portfolio Selection

2022 ◽  
Author(s):  
Dimitris Bertsimas ◽  
Ryan Cory-Wright
Keyword(s):  
Portfolio Selection ◽  
Minimum Variance ◽  
Outer Approximation ◽  
Approximation Procedure ◽  
Expected Return ◽  
Risky Assets ◽  
Scalable Algorithm ◽  
Second Order Cone ◽  
Real World Problem ◽  
Sparse Portfolio

The sparse portfolio selection problem is one of the most famous and frequently studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities, and minimum investment constraints. Existing certifiably optimal approaches to this problem have not been shown to converge within a practical amount of time at real-world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic that supplies high-quality warm-starts, and a second heuristic for generating additional cuts that strengthens the root relaxation. We also study the problem’s continuous relaxation, establish that it is second-order cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that a conjunction of the imposition of ridge regularization and the use of the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.

scholarly journals A Mean-Variance Portfolio Selection Model with Interval-Valued Possibility Measures

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yunyun Sui ◽  
Jiangshan Hu ◽  
Fang Ma
Keyword(s):  
Portfolio Selection ◽  
Return Rate ◽  
Selection Model ◽  
Expected Return ◽  
Interval Numbers ◽  
Numerical Example ◽  
Mean Variance Portfolio ◽  
Portfolio Selection Model ◽  
Mean Variance ◽  
Interval Valued

In recent years, fuzzy set theory and possibility theory have been widely used to deal with an uncertain decision environment characterized by vagueness and ambiguity in the financial market. Considering that the expected return rate of investors may not be a fixed real number but can be an interval number, this paper establishes an interval-valued possibilistic mean-variance portfolio selection model. In this model, the return rate of assets is regarded as a fuzzy number, and the expected return rate of assets is measured by the interval-valued possibilistic mean of fuzzy numbers. Therefore, the possibilistic portfolio selection model is transformed into an interval-valued optimization model. The optimal solution of the model is obtained by using the order relations of interval numbers. Finally, a numerical example is given. Through the numerical example, it is shown that, when compared with the traditional possibilistic model, the proposed model has more constraints and can better reflect investor psychology. It is an extension of the traditional possibilistic model and offers greater flexibility in reflecting investor expectations.

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