scholarly journals Time Consistency of the Mean-Risk Problem

2021 ◽  
Author(s):  
Gabriela Kováčová ◽  
Birgit Rudloff
Keyword(s):  
Optimization Problems ◽  
Efficient Frontier ◽  
Time Consistency ◽  
Vector Optimization Problem ◽  
Consistency Property ◽  
The Mean ◽  
Time Inconsistent ◽  
Bellman Principle ◽  
Mean Risk ◽  
General Time

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through a backward recursion. The mean-risk problem is known to be time inconsistent when considered in its scalarized form. However, when left in its original bi-objective form, it turns out to satisfy a more general time consistency property that seems better suited to a vector optimization problem. In “Time Consistency of the Mean-Risk Problem,” Kováĉova and Rudloff introduce a set-valued version of the famous Bellman principle and show that the bi-objective mean-risk problem does satisfy it. Then, the upper image, a set that contains the efficient frontier on its boundary, recurses backward in time. Kováĉova and Rudloff present conditions under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. This opens the door for a new branch in mathematics: dynamic multivariate programming.

scholarly journals Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Qinghai He ◽  
Weili Kong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Value Set ◽  
Set Valued Mapping ◽  
Optimal Value

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

scholarly journals An Improved Teaching-Learning-Based Optimization with the Social Character of PSO for Global Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Feng Zou ◽  
Debao Chen ◽  
Jiangtao Wang
Keyword(s):  
Optimization Problems ◽  
Global Solutions ◽  
Function Optimization ◽  
Improved Method ◽  
Social Character ◽  
The Social ◽  
Teaching Learning Based Optimization ◽  
The Mean ◽  
The Individual ◽  
Teaching Learning

An improved teaching-learning-based optimization with combining of the social character of PSO (TLBO-PSO), which is considering the teacher’s behavior influence on the students and the mean grade of the class, is proposed in the paper to find the global solutions of function optimization problems. In this method, the teacher phase of TLBO is modified; the new position of the individual is determined by the old position, the mean position, and the best position of current generation. The method overcomes disadvantage that the evolution of the original TLBO might stop when the mean position of students equals the position of the teacher. To decrease the computation cost of the algorithm, the process of removing the duplicate individual in original TLBO is not adopted in the improved algorithm. Moreover, the probability of local convergence of the improved method is decreased by the mutation operator. The effectiveness of the proposed method is tested on some benchmark functions, and the results are competitive with respect to some other methods.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

Characterization of stochastic equilibrium controls by the Malliavin calculus

2021 ◽  
pp. 2150054
Author(s):  
Jiang Yu Nguwi ◽  
Nicolas Privault
Keyword(s):  
Malliavin Calculus ◽  
Linear Quadratic ◽  
Merton Problem ◽  
Classical Duality ◽  
The Mean ◽  
Time Inconsistent ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Quadratic Case

We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem.

Strong Time-Consistency of a Core: An Application to the Pollution Control Problem in Eastern Siberia

2021 ◽  
Author(s):  
Ekaterina V. Gromova ◽  
Polina I. Barsuk ◽  
Shimai Su
Keyword(s):  
Absorption Coefficient ◽  
Pollution Control ◽  
Time Consistency ◽  
Model Parameters ◽  
Eastern Siberia ◽  
Linear Quadratic ◽  
The Core ◽  
Consistency Property ◽  
Strong Time Consistency ◽  
The Russian Federation

In this paper, we study the (strong) time-consistency property of the core for a linear-quadratic differential game of pollution control with nonzero absorption coefficient and real values of the model parameters. The values of parameters are evaluated based on the data for the largest aluminum enterprises of Eastern Siberia region of the Russian Federation for the year 2016. The obtained results are accompanied with illustrations.

Conclusion

2020 ◽  
pp. 248-250
Author(s):  
Paul Weirich
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Risk Principle ◽  
Expected Utility Maximization ◽  
The Mean ◽  
Mean Risk

Recognizing that an act’s risk is a consequence of the act yields a version of expected-utility maximization that does not need adjustments for risk in addition to the probabilities and utilities of possible outcomes. This treatment of an act’s risk justifies the expected-utility principle, and the mean-risk principle, for evaluation of an act. Rational attitudes to risks explain the rationality of acting in accord with the principles. They ground the separability relations that support the principles. The expected-utility principle justifies a substantive, and not just a representational, version of the decision principle of expected-utility maximization. Consequently, the principle governs a single choice and not just sets of choices. It demands more than consistency of the choices in a set. It demands that each choice follow the agent’s preferences, and these preferences explain the rationality of a choice that complies with the principle.

Regulation of Risks

2020 ◽  
pp. 196-220
Author(s):  
Paul Weirich
Keyword(s):  
Cooperative Games ◽  
Regulatory Agencies ◽  
Multiple Agents ◽  
The Public ◽  
The People ◽  
Simplifying Assumptions ◽  
Regulatory Measures ◽  
The Mean ◽  
The Law ◽  
Mean Risk

Governments regulate risks on behalf of the people they serve. Given that regulatory agencies aim for regulatory measures that the public would endorse if rational and informed, the mean-risk method of evaluating acts provides valuable guidance. It offers a way of constructing for a citizen informed probability and utility assignments for a regulation’s possible outcomes, and using these assignments to obtain for the citizen an informed utility assignment for the regulation. The theory of cooperative games combines the utility assignments of multiple agents to support a collective act, and under simplifying assumptions, supports an act that maximizes collective utility, defined as a sum of the act’s utilities for the agents, in the tradition of utilitarianism. This approach to regulation accommodates acts targeting information-sensitive, evidential risks as well as acts targeting physical risks. Verification of a reduction in an evidential risk can meet the standards of objectivity that the law adopts.

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