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An Application of Maximal Exponential Models to Duality Theory.
Marina Santacroce1, Paola Siri1, Barbara Trivellato1
1Dipartimento di Scienze Matematiche "G.L. Lagrange", Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Maximal exponential models define a polar cone in convex optimization. This leads to a financial minimax theorem for portfolio exponential utility maximization.
Area of Science:
- Mathematical Optimization
- Financial Mathematics
Background:
- Convex optimization frameworks are essential for modeling complex systems.
- Understanding polar cones is crucial for analyzing optimization problems.
Purpose of the Study:
- To characterize a suitable polar cone using maximal exponential models.
- To develop a financial application demonstrating the theoretical results.
Main Methods:
- Utilizing maximal exponential models.
- Applying convex optimization techniques.
- Deriving a duality minimax theorem.
Main Results:
- Successfully characterized a polar cone within the mathematical framework.
- Established a duality minimax theorem for exponential utility maximization.
- Provided a direct financial application of the theoretical findings.
Conclusions:
- The study provides a novel approach to defining polar cones in optimization.
- The financial application highlights the practical relevance of the theoretical framework.
- The duality minimax theorem offers new insights into portfolio optimization.
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