Higher-Order Stochastic Dominance Constraints in Optimization

This repository provides an efficient framework to solve optimization problems involving higher-order stochastic dominance (HOSD) constraints. These constraints are often uncountably infinite, but this implementation reduces the problem to a finite set of test points, making it computationally feasible.

Key Features

• Finite Reduction of Constraints:
  • We simplify uncountable stochastic dominance constraints into a finite, computationally verifiable set of test points.
• Optimization Framework:
  • Incorporates theoretical verification setup using Newton method
• Two Variants:
  • Objective: Maximize Expected Return
  • Objective: Minimize Risk measure

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Getting Started

Prerequisites

Before running the code, ensure you have the following installed:

• Julia (v1.7 or later)
• Dependencies for scientific computation: LinearAlgebra, ForwardDiff

Install dependencies via Julia's package manager:

using Pkg
Pkg.add("LinearAlgebra")
Pkg.add("ForwardDiff")

Code Structure

The directory is organized as follows:

File/Folder	Purpose
src/	Contains source code, including the main implementation and utilities.
Dataset/	Provides datasets used for testing and experiments.
Prominent Algorithm/	Contains implementations of prominent stochastic dominance approaches.
README.md	Overview and instructions for the project.

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Citing This Work

If you use this code, please cite the corresponding research paper:

TODO: Add link to the paper

This paper comprehensively explains the implementation and methodology of our proposed approach.

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Contributions

We welcome contributions! Please feel free to open an issue or submit a pull request if you have suggestions, bug reports, or feature requests.