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Interval-based stochastic dominance: theoretical framework and application to portfolio choices.
Jia Liu1,2, Zhiping Chen1,2, Giorgio Consigli3,4
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi People's Republic of China.
Annals of Operations Research
|September 6, 2021
Summary
We introduce interval-based stochastic dominance (ISD), a new preference relation that bridges different orders of stochastic dominance (SD). ISD offers a flexible framework for financial decision-making and portfolio optimization.
Area of Science:
- Decision Theory
- Financial Mathematics
- Optimization
Background:
- Stochastic dominance (SD) provides a framework for comparing risky choices.
- Existing SD orders (e.g., first-order, second-order) represent specific risk preferences.
- A need exists for more flexible preference relations in financial decision-making.
Purpose of the Study:
- Introduce and define interval-based stochastic dominance (ISD).
- Explore the relationship between ISD and traditional SD orders.
- Investigate the application of ISD in optimal financial allocation and portfolio selection.
Main Methods:
- Define ISD by selecting reference points, creating a continuum of preferences.
- Analyze the relationship between ISD, SD orders, risk measures, and utility functions.
- Formulate and solve ISD-constrained optimization problems with discrete random variables.
Main Results:
- ISD generalizes and spans preferences between kth and (k+1)th order SD.
- ISD of order 1 spans first- to second-order SD; order 2 spans second- to third-order SD.
- The study provides a detailed formulation and application of ISD in portfolio selection.
Conclusions:
- ISD offers a novel and flexible approach to modeling preferences in decision theory.
- ISD has significant implications for optimal financial allocation and portfolio optimization.
- The framework is applicable to problems involving discrete random variables.
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