scholarly journals Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Ye Wang ◽  
Yanju Chen ◽  
YanKui Liu
Keyword(s):  
Convex Programming ◽  
Portfolio Selection ◽  
Optimization Problem ◽  
Fuzzy Variable ◽  
Optimization Method ◽  
General Purpose ◽  
Convex Programming Problem ◽  
Fuzzy Variables ◽  
Return Rates ◽  
Fuzzy Expected Value

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

scholarly journals Near-Optimal Guidance with Impact Angle and Velocity Constraints Using Sequential Convex Programming

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Pei Pei ◽  
Jiang Wang
Keyword(s):  
Convex Programming ◽  
Optimization Problem ◽  
Angle Of Attack ◽  
Control Variable ◽  
Optimization Theory ◽  
Impact Angle ◽  
General Purpose ◽  
Problem Solver ◽  
Sequential Convex Programming ◽  
Velocity Constraints

This paper proposes a near-optimal air-to-ground missile guidance law with impact angle and impact velocity constraints based on sequential convex programming. A realistic aerodynamic model is introduced into the problem formulation, such that traditional optimization theory cannot obtain an analytical solution to the optimization problem under state constraints. The original problem is considered as an optimization problem, and the angle of attack is replaced with the angle of attack rate as a new control variable to reconstruct the problem and simplify the solving process. Next, the independent variable is changed in the differential equations to linearize and discretize the problem such that the reconstructed problem can be solved using sequential convex programming. The results obtained by numerical simulations confirmed that the proposed algorithm is valid and faster than the general-purpose nonlinear optimal control problem solver. Finally, it was verified that different impact angles and impact velocities were achieved.

The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection

2020 ◽  
Vol 16 (02) ◽  
pp. 271-290
Author(s):  
Justin Dzuche ◽  
Christian Deffo Tassak ◽  
Jules Sadefo Kamdem ◽  
Louis Aimé Fono
Keyword(s):  
Linear Combination ◽  
Portfolio Selection ◽  
Fuzzy Variable ◽  
Expected Value ◽  
Mathematical Science ◽  
Optimal Portfolios ◽  
Fuzzy Variables ◽  
Convex Linear Combination

Possibility, necessity and credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [L. Yang and K. Iwamura, Applied Mathematical Science 2(46) (2008) 2271–2288] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy variable based on that measure, namely, expected value, variance, semi-variance, skewness, kurtosis and semi-kurtosis. We determine some properties of these characteristics and we compute them for trapezoidal and triangular fuzzy variables. We display their application for the determination of optimal portfolios when assets returns are described by triangular or trapezoidal fuzzy variables.

scholarly journals Dantzig Type Optimization Method with Applications to Portfolio Selection

2019 ◽  
Vol 11 (11) ◽  
pp. 3216
Author(s):  
Seyoung Park ◽  
Eun Ryung Lee ◽  
Sungchul Lee ◽  
Geonwoo Kim
Keyword(s):  
Portfolio Selection ◽  
Optimization Problem ◽  
Simulated Data ◽  
Optimization Method ◽  
Selection Methods ◽  
Information Ratio ◽  
The West ◽  
The North ◽  
Benchmark Portfolio ◽  
Reduce Risk

This paper investigates a novel optimization problem motivated by sparse, sustainable and stable portfolio selection. The existing benchmark portfolio via the Dantzig type optimization is used to construct a sparse, sustainable and stable portfolio. Based on the formulations, this paper proposes two portfolio selection methods, west and north portfolio selection, and investigates their empirical properties. Numerical results presented for 12 datasets and various simulated data show that the west selection can reduce risk, and the north selection may outperform the benchmark as to risk-adjusted returns (based on, e.g., information ratio and Sharpe ratio).

MEAN-SEMIVARIANCE MODELS FOR PORTFOLIO OPTIMIZATION PROBLEM WITH MIXED UNCERTAINTY OF FUZZINESS AND RANDOMNESS

2013 ◽  
Vol 21 (supp01) ◽  
pp. 127-139 ◽  
Author(s):  
ZHONGFENG QIN ◽  
DAVID Z. W. WANG ◽  
XIANG LI
Keyword(s):  
Portfolio Optimization ◽  
Optimization Problem ◽  
Risk Measure ◽  
Fuzzy Variable ◽  
Expected Returns ◽  
Random Fuzzy Variable ◽  
Fuzzy Variables ◽  
The Mean ◽  
Security Returns ◽  
Portfolio Optimization Problem

In practice, security returns cannot be accurately predicted due to lack of historical data. Therefore, statistical methods and experts' experience are always integrated to estimate future security returns, which are hereinafter regarded as random fuzzy variables. Random fuzzy variable is a powerful tool to deal with the portfolio optimization problem including stochastic parameters with ambiguous expected returns. In this paper, we first define the semivariance of random fuzzy variable and prove its several properties. By considering the semivariance as a risk measure, we establish the mean-semivariance models for portfolio optimization problem with random fuzzy returns. We design a hybrid algorithm with random fuzzy simulation to solve the proposed models in general cases. Finally, we present a numerical example and compare the results to illustrate the mean-semivariance model and the effectiveness of the algorithm.

scholarly journals Optimal Decisions for Prepositioning Emergency Supplies Problem with Type-2 Fuzzy Variables

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Xuejie Bai
Keyword(s):  
Value At Risk ◽  
Fuzzy Variable ◽  
General Purpose ◽  
Mixed Integer ◽  
Fuzzy Variables ◽  
Logistics Network ◽  
Disaster Relief Operations ◽  
Proposed Model ◽  
Relief Operations

Prepositioning emergency supplies serves an important function in disaster relief operations. This paper presents a new class of fuzzy prepositioning emergency supplies model for three-echelon humanitarian logistics network, in which the postdisaster acquisition and transportation costs, the suppliers’ supply, and affected areas’ demand are uncertain and characterized by type-2 fuzzy variables with known possibility distributions. Since the inherent complexity of fuzzy prepositioning problem may be troublesome, the existing methods are no longer effective in dealing with the proposed model directly. We first derive the optimistic and pessimistic values formula for credibility value-at-risk (CVaR) reduced fuzzy variable of type-2 trapezoidal fuzzy variable. On the basis of formula obtained, we can convert original fuzzy prepositioning model into its equivalent parametric mixed integer programming form, which can be solved by conventional algorithms or general-purpose software. Finally, some numerical experiments have been performed to illustrate the effectiveness of the proposed model and solution strategy.

The Improvement of Newton Method and the Validation of Optimization Idea of Blind Walking Repeatedly

2011 ◽  
Vol 250-253 ◽  
pp. 4061-4064
Author(s):  
Chun Ling Zhang
Keyword(s):  
Saddle Point ◽  
Newton Method ◽  
Optimization Problem ◽  
Initial Point ◽  
Optimization Method ◽  
Maximum Point ◽  
Optimal Result ◽  
Feasible Domain ◽  
Parallel Arithmetic ◽  
Newton Direction

The existence of maximum point, oddity point and saddle point often leads to computation failure. The optimization idea is based on the reality that the optimum towards the local minimum related the initial point. After getting several optimal results with different initial point, the best result is taken as the final optimal result. The arithmetic improvement of multi-dimension Newton method is improved. The improvement is important for the optimization method with grads convergence rule or searching direction constructed by grads. A computational example with a saddle point, maximum point and oddity point is studied by multi-dimension Newton method, damped Newton method and Newton direction method. The importance of the idea of blind walking repeatedly is testified. Owing to the parallel arithmetic of modernistic optimization method, it does not need to study optimization problem with seriate feasible domain by modernistic optimization method.

Parameter study and optimization design of a hat oblique tunnel portal

2021 ◽  
pp. 095440972110140
Author(s):  
Zijian Guo ◽  
Tanghong Liu ◽  
Wenhui Li ◽  
Yutao Xia
Keyword(s):  
High Speed ◽  
Optimization Design ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Method ◽  
Design Parameters ◽  
Parameter Study ◽  
Buffer Structure ◽  
Tunnel Entrance ◽  
The Ideal

The present work focuses on the aerodynamic problems resulting from a high-speed train (HST) passing through a tunnel. Numerical simulations were employed to obtain the numerical results, and they were verified by a moving-model test. Two responses, [Formula: see text] (coefficient of the peak-to-peak pressure of a single fluctuation) and[Formula: see text] (pressure value of micro-pressure wave), were studied with regard to the three building parameters of the portal-hat buffer structure of the tunnel entrance and exit. The MOPSO (multi-objective particle swarm optimization) method was employed to solve the optimization problem in order to find the minimum [Formula: see text] and[Formula: see text]. Results showed that the effects of the three design parameters on [Formula: see text] were not monotonous, and the influences of[Formula: see text] (the oblique angle of the portal) and [Formula: see text] (the height of the hat structure) were more significant than that of[Formula: see text] (the angle between the vertical line of the portal and the hat). Monotonically decreasing responses were found in [Formula: see text] for [Formula: see text] and[Formula: see text]. The Pareto front of [Formula: see text] and[Formula: see text]was obtained. The ideal single-objective optimums for each response located at the ends of the Pareto front had values of 1.0560 for [Formula: see text] and 101.8 Pa for[Formula: see text].

scholarly journals An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm

2017 ◽  
Author(s):  
Yann Poirette ◽  
Martin Guiton ◽  
Guillaume Huwart ◽  
Delphine Sinoquet ◽  
Jean Marc Leroy
Keyword(s):  
Wind Farm ◽  
Optimization Problem ◽  
Initial Point ◽  
Trust Region ◽  
Optimization Method ◽  
Global Optimum ◽  
Offshore Wind ◽  
Finite Element Software ◽  
Constrained Problems ◽  
Floating Offshore Wind Turbines

IFP Energies nouvelles (IFPEN) is involved for many years in various projects for the development of floating offshore wind turbines. The commercial deployment of such technologies is planned for 2020. The present paper proposes a methodology for the numerical optimization of the inter array cable configuration. To illustrate the potential of such an optimization, results are presented for a case study with a specific floating foundation concept [1]. The optimization study performed aims to define the least expensive configuration satisfying mechanical constraints under extreme environmental conditions. The parameters to be optimized are the total length, the armoring, the stiffener geometry and the buoyancy modules. The insulated electrical conductors and overall sheath are not concerned by this optimization. The simulations are carried out using DeepLines™, a Finite Element software dedicated to simulate offshore floating structures in their marine environment. The optimization problem is solved using an IFPEN in-house tool, which integrates a state of the art derivative-free trust region optimization method extended to nonlinear constrained problems. The latter functionality is essential for this type of optimization problem where nonlinear constraints are introduced such as maximum tension, no compression, maximum curvature and elongation, and the aero-hydrodynamic simulation solver does not provide any gradient information. The optimization tool is able to find various local feasible extrema thanks to a multi-start approach, which leads to several solutions of the cable configuration. The sensitivity to the choice of the initial point is demonstrated, illustrating the complexity of the feasible domain and the resulting difficulty in finding the global optimum configuration.

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