Distributionally robust fractional optimization of probability of exceedance
Researchers Lejeune and Nguyen present a new framework for distributionally robust fractional optimization, focusing on the probability of exceedance, a key risk measure in finance. Their models handle both moment-based and Wasserstein ambiguity sets and reformulate complex chance constraints into solvable forms. A custom algorithm efficiently tackles biconvex cases. Notably, moment-based models excel with few assets, but Wasserstein models outperform as asset numbers grow, boosting Sharpe ratio and returns. More real-world tests are suggested.
What it examines
This paper develops new models to maximize the probability of exceedance, expressed as a ratio of uncertain functions, using distributionally robust optimization. It covers both moment and Wasserstein ambiguity sets, various function types, and provides efficient algorithms for solving these complex financial and engineering problems.
What it concludes
The proposed methods improve performance in financial applications, such as portfolio optimization, especially for different asset sizes. Moment-based models work better for small asset sets, while Wasserstein-based models scale well for larger ones. These results can help manage risk and returns in finance and other uncertain decision-making fields.
Evidence objects
Lejeune and Nguyen introduce a versatile framework for distributionally robust fractional optimization, reformulating complex chance-constrained problems into tractable forms and designing a custom algorithm for biconvex cases in asset allocation.
key_findings bullet 1 · key_findings · validation V0
Their models handle both moment-based and Wasserstein ambiguity sets, supporting linear and quadratic ratios. Notably, they efficiently solve integer and continuous problems, advancing computational methods in financial risk management.
key_findings bullet 2 · key_findings · validation V0
Surprisingly, moment-based models outperform Wasserstein models in small asset universes, but Wasserstein models excel as asset numbers grow, boosting Sharpe ratio and cumulative returnhighlighting practical relevance and future research potential.
key_findings bullet 3 · key_findings · validation V0
This paper introduces a novel framework for distributionally robust fractional optimization of probability of exceedance, integrating moment and Wasserstein ambiguity sets, diverse functional forms, and tractable biconvex reformulations. Its originality lies in generalizing across ambiguity sets and supports, with compelling empirical results in portfolio optimization, offering significant methodological and computational advancements.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
- … and cumulative return when the asset universes’ size is small. In contrast, Wasserstein-based models exhibit superior performance and scale better as the size of the asset …
Source row: 627 · abstract type: snippet