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Mean-deviation analysis in the theory of choice
Bogdan Grechuk1, Anton Molyboha, Michael Zabarankin
1Department of Mathematics, University of Leicester, LE1 7RH, UK.
Summary
This study explores mean-deviation analysis within choice under uncertainty theory. It establishes axiomatic foundations for coherent risk measures and mean-deviation analysis, offering resolutions to paradoxes in rational choice and risk sharing.
Area of Science:
- Decision Theory
- Financial Mathematics
- Behavioral Economics
Background:
- The theory of choice under uncertainty models rational preferences for random outcomes.
- Coherent risk measures and dual utility theory provide frameworks for analyzing risk.
- Mean-deviation analysis offers an alternative approach to risk assessment.
Purpose of the Study:
- To examine mean-deviation analysis within the theory of choice under uncertainty.
- To establish axiomatic foundations for coherent risk measures and mean-deviation analysis.
- To discuss paradoxes and resolutions in axiomatic frameworks for risk analysis.
Main Methods:
- Axiomatic analysis of preference relations under uncertainty.
- Relaxation of axioms from dual utility theory to derive coherent risk measures.
- Further relaxation of axioms to establish mean-deviation analysis.
- Exploration of paradoxes and their resolutions within these theoretical frameworks.
Main Results:
- An axiomatic foundation for coherent risk measures is derived by relaxing dual utility axioms.
- Mean-deviation analysis is established through a further relaxation of these axioms.
- Paradoxes inherent in these axiomatic sets are identified and potential resolutions are discussed.
Conclusions:
- Mean-deviation analysis can be axiomatically grounded within choice under uncertainty.
- The study provides a theoretical link between dual utility, coherent risk measures, and mean-deviation analysis.
- Applications in optimal risk sharing and portfolio selection are considered within a rational choice context.
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