scholarly journals The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 133 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Fuzzy Number ◽  
Mixed Models ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Random Variables ◽  
Background Risk ◽  
Investment Risk ◽  
Approximate Formulas

In this paper, several portfolio choice models are studied: a purely possibilistic model in which the return of the risky is a fuzzy number, and four models in which the background risk appears in addition to the investment risk. In these four models, risk is a bidimensional vector whose components are random variables or fuzzy numbers. Approximate formulas of the optimal allocation are obtained for all models, expressed in terms of some probabilistic or possibilistic moments, depending on the indicators of the investor preferences (risk aversion, prudence).

scholarly journals A Portfolio Choice Problem in the Framework of Expected Utility Operators

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 669 ◽  
Author(s):  
Irina Georgescu ◽  
Louis Aimé Fono
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Approximate Calculation ◽  
Optimization Problem ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
General Context ◽  
Abstract Theory ◽  
Choice Problem

Possibilistic risk theory starts from the hypothesis that risk is modeled by fuzzy numbers. In particular, in a possibilistic portfolio choice problem, the return of a risky asset will be a fuzzy number. The expected utility operators have been introduced in a previous paper to build an abstract theory of possibilistic risk aversion. To each expected utility operator, one can associate the notion of possibilistic expected utility. Using this notion, we will formulate in this very general context a possibilistic portfolio choice problem. The main results of the paper are two approximate calculation formulas for the corresponding optimization problem. The first formula approximates the optimal allocation with respect to risk aversion and investor’s prudence, as well as the first three possibilistic moments. Besides these parameters, in the second formula, the temperance index of the utility function and the fourth possibilistic moment appear.

scholarly journals Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
S. K. Barik ◽  
M. P. Biswal
Keyword(s):  
Quadratic Programming ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Random Variables ◽  
Solution Procedure ◽  
Triangular Fuzzy Number ◽  
Probabilistic Constraints ◽  
Model Parameters ◽  
Trapezoidal Fuzzy Number

We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.

A NEW NOTION OF POSSIBILISTIC COVARIANCE

2013 ◽  
Vol 09 (01) ◽  
pp. 1-11 ◽  
Author(s):  
IRINA GEORGESCU ◽  
JANI KINNUNEN
Keyword(s):  
Risk Aversion ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Expected Value

Possibilistic indicators of fuzzy numbers (expected value, variance, and covariance) are an efficient instrument in the modeling of uncertainty phenomena. Various models of uncertainty phenomena have led to several notions of variance and covariance. In particular, the possibilistic models of risk aversion previously studied by one of the authors imposed a notion of variance of a fuzzy number different from those existing in the literature. In this paper, a new notion of covariance of two fuzzy numbers corresponding to the possibilistic variance mentioned is studied. This possibilistic covariance can be used, e.g. in models of possibilistic risk aversion with many parameters.

scholarly journals A possibilistic and probabilistic approach to precautionary saving

2017 ◽  
Vol 64 (3) ◽  
pp. 273-295 ◽  
Author(s):  
Irina Georgescu ◽  
Adolfo Cristóbal-Campoamor ◽  
Ana Lucia-Casademunt
Keyword(s):  
Fuzzy Number ◽  
Mixed Models ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Precautionary Saving ◽  
Optimal Choice ◽  
Background Risk ◽  
Precautionary Savings ◽  
Income Risk ◽  
Optimal Saving

This paper proposes two mixed models to study a consumer?s optimal saving in the presence of two types of risk: income risk and background risk. In the first model, income risk is represented by a fuzzy number and background risk by a random variable. In the second model, income risk is represented by a random variable and background risk by a fuzzy number. For each model, three notions of precautionary savings are defined as indicators of the extra saving induced by income and background risk on the consumer?s optimal choice. In conclusion, we can characterize the conditions that allow for extra saving relative to optimal saving under certainty, even when a certain component of risk is modelled using fuzzy numbers.

Relative Risk Aversion and Portfolio Choice

2005 ◽  
Author(s):  
Pablo Muñoz Ceballos ◽  
Esteban Flores Díaz
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Relative Risk Aversion

Portfolio choice with skewness preference and wealth-dependent risk aversion

2019 ◽  
Vol 19 (11) ◽  
pp. 1905-1919
Author(s):  
Congming Mu ◽  
Weidong Tian ◽  
Jinqiang Yang
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Skewness Preference

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

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