scholarly journals How the Investor’s Risk Preferences Influence the Optimal Allocation in a Credibilistic Portfolio Problem

2019 ◽  
Vol 7 (4) ◽  
pp. 317-329
Author(s):  
Irina Georgescu ◽  
Jani Kinnunen
Keyword(s):  
Utility Function ◽  
Portfolio Choice ◽  
Expected Utility ◽  
Optimal Allocation ◽  
Fuzzy Variable ◽  
Risky Asset ◽  
Credibility Theory ◽  
Fuzzy Variables ◽  
Portfolio Problem ◽  
Approximation Calculation

Abstract A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and how, combined with the utility function defines a notion of expected utility. In this paper the risk is a fuzzy variable and the notion of expected utility is defined in the setting of Liu’s credibility theory. Thus, the portfolio choice problem is formulated as an optimization problem in which the objective function is a credibilistic expected utility. Different approximation calculation formulas for the optimal allocation of the credibilistic risky asset are proved. These formulas contain two types of parameters: Various credibilistic moments associated with fuzzy variables (expected value, variance, skewness and kurtosis) and the risk aversion, prudence and temperance indicators of the utility function.

Computing the Risk Indicators in Fuzzy Systems

2012 ◽  
Vol 5 (4) ◽  
pp. 63-84 ◽  
Author(s):  
Irina Georgescu
Keyword(s):  
Risk Aversion ◽  
Risk Premium ◽  
Stochastic Dominance ◽  
Probabilistic Models ◽  
Fuzzy Variable ◽  
Risk Indicators ◽  
Credibility Theory ◽  
Fuzzy Variables ◽  
Risk Situation ◽  
Definition Of

The modeling of complex risk situations imposes the existence of multiple ways to represent the risk and compare the risk situations between them. In probabilistic models, risk is described by random variables and risk situations are compared by stochastic dominance. In possibilistic or credibilistic models, risk is represented by fuzzy variables. This paper concerns three indicators of dominance associated with fuzzy variables. This allows the definition of three notions of fuzzy dominance: dominance in possibility, dominance in necessity and dominance in credibility. These three types of dominance are possibilistic and credibilistic versions of stochastic dominance. Each type offers a modality of ranking risk situations modeled by fuzzy variables. In the paper some properties of the three indicators of dominance are proved and relations between the three types of fuzzy dominance are established. For triangular fuzzy numbers formulas for the computation of these indicators are obtained. The paper also contains a contribution on a theory of risk aversion in the context of credibility theory. Using the credibilistic expected utility a notion of risk premium is defined as a measure of risk aversion of an agent in front of a risk situation described by a fuzzy variable and an approximate calculation formula of this indicator is proved.

scholarly journals Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangfeng Li ◽  
Qiong Wu ◽  
Zhiqiang Ye ◽  
Shunming Zhang
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Comparative Statics ◽  
Risky Asset ◽  
Stochastic Orders ◽  
Monotone Likelihood Ratio ◽  
Changes In Risk ◽  
The Right ◽  
Monotone Probability ◽  
The Relationship

As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion.

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 A FUZZY BASED APPROACH FOR EARLY REQUIREMENT PRIORITIZATION

2015 ◽  
Vol 15 (2) ◽  
pp. 6480-6490
Author(s):  
Mohd Muqeem ◽  
Dr. Md. Rizwan Beg
Keyword(s):  
Software Development ◽  
Early Phase ◽  
Fuzzy Variable ◽  
Requirement Engineering ◽  
Expected Value ◽  
Inference System ◽  
Complex Time ◽  
Fuzzy Variables ◽  
Expected Value Operator ◽  
Requirement Prioritization

The importance of the prioritization in commercial software development has been analyzed by many researchers. The gathered requirements are required to be put into an order of some priority. In other words we can say that there is a need to prioritize the requirements. It is evident that most of the approaches and techniques proposed in recent research to prioritize the requirements have not been widely adopted. These approaches are too complex, time consuming, or inconsistent and difficult to implement In this paper we propose a fuzzy based approach for requirement prioritization in which  requirement are prioritized in early phase of requirement engineering as post elicitation step. This category of prioritization is known as early requirement prioritization. The proposed fuzzy based approach considers the nature of requirements by modeling their attributes as fuzzy variables. As such, these variables are integrated into a fuzzy based inference system in which the requirements represented as input attributes and ranked via the expected value operator of a fuzzy variable.

scholarly journals Consistency and Heterogeneity of Individual Behavior under Uncertainty

2007 ◽  
Vol 97 (5) ◽  
pp. 1921-1938 ◽  
Author(s):  
Syngjoo Choi ◽  
Raymond Fisman ◽  
Douglas Gale ◽  
Shachar Kariv
Keyword(s):  
Utility Function ◽  
Portfolio Choice ◽  
Individual Behavior ◽  
Parameter Estimates ◽  
Individual Subject ◽  
Individual Level ◽  
Study Behavior ◽  
The Individual ◽  
Two Parameter ◽  
Good Interpretation

By using graphical representations of simple portfolio choice problems, we generate a very rich dataset to study behavior under uncertainty at the level of the individual subject. We test the data for consistency with the maximization hypothesis, and we estimate preferences using a two-parameter utility function based on Faruk Gul (1991). This specification provides a good interpretation of the data at the individual level and can account for the highly heterogeneous behaviors observed in the laboratory. The parameter estimates jointly describe attitudes toward risk and allow us to characterize the distribution of risk preferences in the population. (JEL D11, D14, D81, G11)

OPTIMAL PORTFOLIO UNDER STATE-DEPENDENT EXPECTED UTILITY

2018 ◽  
Vol 21 (03) ◽  
pp. 1850013 ◽  
Author(s):  
CAROLE BERNARD ◽  
STEVEN VANDUFFEL ◽  
JIANG YE
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Loss Aversion ◽  
Reference Point ◽  
Joint Distribution ◽  
Optimal Portfolio ◽  
Characterization Result ◽  
Terminal Wealth ◽  
Utility Maximizer ◽  
State Dependent

We derive the optimal portfolio for an expected utility maximizer whose utility does not only depend on terminal wealth but also on some random benchmark (state-dependent utility). We then apply this result to obtain the optimal portfolio of a loss-averse investor with a random reference point (extending a result of Berkelaar et al. (2004) Optimal portfolio choice under loss aversion, The Review of Economics and Statistics 86 (4), 973–987). Clearly, the optimal portfolio has some joint distribution with the benchmark and we show that it is the cheapest possible in having this distribution. This characterization result allows us to infer the state-dependent utility function that explains the demand for a given (joint) distribution.

A Bayesian method to estimate the optimal threshold of a marker used to select patients' treatment

2019 ◽  
Vol 29 (1) ◽  
pp. 29-43
Author(s):  
Yoann Blangero ◽  
Muriel Rabilloud ◽  
René Ecochard ◽  
Fabien Subtil
Keyword(s):  
Utility Function ◽  
Expected Utility ◽  
Treatment Options ◽  
Growth Factor Receptor ◽  
Credible Interval ◽  
Optimal Threshold ◽  
Selection Marker ◽  
Large Sample Size ◽  
Marker Distribution ◽  
Definition Of

The use of a quantitative treatment selection marker to choose between two treatment options requires the estimate of an optimal threshold above which one of these two treatments is preferred. Herein, the optimal threshold expression is based on the definition of a utility function which aims to quantify the expected utility of the population (e.g. life expectancy, quality of life) by taking into account both efficacy (success or failure) and toxicity of each treatment option. Therefore, the optimal threshold is the marker value that maximizes the expected utility of the population. A method modelling the marker distribution in patient subgroups defined by the received treatment and the outcome is proposed to calculate the parameters of the utility function so as to estimate the optimal threshold and its 95% credible interval using the Bayesian inference. The simulation study found that the method had low bias and coverage probability close to 95% in multiple settings, but also the need of large sample size to estimate the optimal threshold in some settings. The method is then applied to the PETACC-8 trial that compares the efficacy of chemotherapy with a combined chemotherapy + anti-epidermal growth factor receptor in stage III colorectal cancer.

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