scholarly journals Quasi-Arithmetic Type Mean Generated by the Generalized Choquet Integral

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2104
Author(s):  
Sebastian Wójcik
Keyword(s):  
Utility Theory ◽  
Symmetry Property ◽  
Choquet Integral ◽  
General Setting ◽  
Expected Utility Theory ◽  
Arithmetic Mean ◽  
Arithmetic Means ◽  
Insurance Contracts ◽  
Positive Homogeneity

It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in a utility-based insurance contracts pricing. In this paper, we introduce and study the quasi-arithmetic type mean in a more general setting, namely with the expected value being replaced by the generalized Choquet integral. We show that a functional that is defined in this way is a mean. Furthermore, we characterize the equality, positive homogeneity, and translativity in this class of means.

STATE REGULATION OF THE FINANCIAL SERVICES MARKET IN UKRAINE

2018 ◽  
Vol 1 (11) ◽  
pp. 30-47
Author(s):  
Lyudmila Nikolayevna Akimova ◽  
Alla Vasilievna Lysachok
Keyword(s):  
Life Insurance ◽  
Financial Services ◽  
Credit Unions ◽  
State Regulation ◽  
The State ◽  
Existing Problems ◽  
Insurance Contracts ◽  
State Pension

The essence of such concepts is “financial service”, “financial ser- vices market”, and “participants of the financial services market”; determined the purpose of state regulation of the financial services market; forms of state regu- lation of the financial services market; financial services that are present in the financial services market; the structure of state regulation bodies of the financial services market in Ukraine is given; The role of state bodies in the regulation of the financial services market was studied; to characterize the regulatory le- gal regulation of the financial services market in Ukraine; the main problems of functioning of the domestic market of financial services are revealed; ways to solve existing problems. It is grounded that the state regulation of financial ser- vices markets consists in the state’s implementation of a set of measures aimed at regulating and overseeing financial services markets to protect the interests of financial services consumers and preventing crisis phenomena. It is concluded that the financial services market is an important element of the development of the economy as a whole, in particular, it concerns not only the state but also society. We must understand that when this market is settled, that is, all bodies that carry out state regulation are competent in their powers, only then will we make informed, effective decisions about the normal and effective functioning of the RFP. It is important that the data of the subjects of control do not overlap, their activities should be fixed at the legislative level. It is also worth bearing in mind that appropriate conditions must be created to create compensatory mecha- nisms in the financial services markets by developing a system for guarante- eing deposits and providing for payments under long-term life insurance contracts, non-state pension provisions, deposits with deposit accounts to credit unions, etс.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals Cumulative Prospect Theory Version with Fuzzy Values of Outcome Estimates

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 72
Author(s):  
Oleg Uzhga-Rebrov ◽  
Peter Grabusts
Keyword(s):  
Prospect Theory ◽  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
Development History ◽  
Decisions Under Risk ◽  
History Of ◽  
Main Factors ◽  
Theoretical Foundations

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained.

Norm-Endorsement Utilitarianism and the Nature of Utility

1996 ◽  
Vol 12 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Jonathan Baron
Keyword(s):  
Expected Utility ◽  
Utility Theory ◽  
Expected Utility Theory ◽  
Interpersonal Comparison ◽  
Moral Norms ◽  
Moral Principles ◽  
Future Goals ◽  
Equal Consideration

In this article, I shall suggest an approach to the justification of normative moral principles which leads, I think, to utilitarianism. The approach is based on asking what moral norms we would each endorse if we had no prior moral commitments. I argue that we would endorse norms that lead to the satisfaction of all our nonmoral values or goals. The same approach leads to a view of utility as consisting of those goals that we would want satisfied. In the second half of the article, I examine the implication of this view for several issues about the nature of utility, such as the use of past and future goals. The argument for utilitarianism is not completed here. The rest of it requires a defense of expected-utility theory, of interpersonal comparison, and of equal consideration (see Baron, 1993; Broome, 1991).

The design of pension contracts: on the perspective of customers

2018 ◽  
Vol 13 (2) ◽  
pp. 219-240 ◽  
Author(s):  
Zhaoxun Mei
Keyword(s):  
Young People ◽  
Utility Theory ◽  
Asset Price ◽  
Expected Utility Theory ◽  
Cumulative Prospect Theory ◽  
The Other ◽  
Risky Assets ◽  
Distribution Rule ◽  
Similar Product ◽  
Guarantee Rate

AbstractThis paper introduces a new pension contract which provides a smoothed return for the customer. The new contract protects customers from adverse asset price movements while keeping the potential of positive returns. It has a transparent structure and clear distribution rule, which can be easily understood by the customer. We compare the new contract to two other contracts under Cumulative Prospect Theory (CPT); one has a similar product structure but without guarantees and the other provides the same guarantee rate but with a different structure. The results show that the new contract is the most attractive contract for a CPT-maximising customer. Yet, we find different results if we let the customer be an Expected Utility Theory-maximising one. Moreover, this paper presents the static optimal portfolio for an individual customer. The results conform to the traditional pension advice that young people should invest more of their money in risky assets while older people should put more money in less risky assets.

Housing Market Search Behavior and Expected Utility Theory: 1. Measuring Preferences for Housing

1982 ◽  
Vol 14 (5) ◽  
pp. 681-698 ◽  
Author(s):  
T R Smith ◽  
W A V Clark
Keyword(s):  
Los Angeles ◽  
Housing Market ◽  
Expected Utility ◽  
Utility Theory ◽  
House Price ◽  
Expected Utility Theory ◽  
Utility Functions ◽  
Future Search ◽  
Space Construction ◽  
Market Search

This is the first of two papers examining housing market search in a Los Angeles market. In this paper, we derive and analyze utility functions for housing for each individual in two groups of subjects. The utility functions are derived from an experimental setting, in which house price, floor space, construction quality, and neighborhood quality are varied. The functions are found to be essentially compatible with a linear model. They are used to predict the ratings of real houses and the ratings of the expected value of future search. These ratings are compared with actual ratings obtained from subjects during search. The results suggest that the actual or predicted ratings may be employed in a direct test of a simple expected utility theory of search, and further research along these lines appears justified.

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