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A data-driven robust EVaR-PC with application to portfolio management.

Qingyun He1, Chuanyang Hong2

  • 1School of Business Administration, The Southwestern University of Finance and Economics, Chengdu, China.

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This summary is machine-generated.

This study introduces a new method for robust chance constrained optimization, combining distributionally robust optimization and chance constraints. The novel EVaR-PC approximation offers a less conservative and more practical approach for decision-making under uncertainty.

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Area of Science:

  • Optimization Theory
  • Decision Science
  • Financial Mathematics

Background:

  • Robust Chance Constrained Optimization Problems (RCCOP) integrate Distributionally Robust Optimization (DRO) and Chance Constraints (CC) for modeling uncertainty.
  • Chance Constraints (CC), equivalent to Value-at-Risk (VaR), are often approximated by risk measures like Entropic Value-at-Risk (EVaR) or Conditional Value-at-Risk (CVaR) for tractability.
  • Distributionally Robust Optimization (DRO) handles uncertainty by considering partial information about probability distributions rather than assuming a known true distribution.

Purpose of the Study:

  • To develop a novel approximation, EVaR-PC, based on EVaR for Chance Constraints (CC).
  • To evaluate the proposed EVaR-PC approximation within a discrepancy-based ambiguity set using Wasserstein distance.
  • To demonstrate the practical advantages of the EVaR-PC method in portfolio management.

Main Methods:

  • Development of a new EVaR-PC approximation for Chance Constraints (CC).
  • Evaluation of EVaR-PC using a discrepancy-based ambiguity set defined by Wasserstein distance.
  • Application and experimental validation in the domain of portfolio management.

Main Results:

  • The EVaR-PC approximation is theoretically less conservative than standard EVaR.
  • The Wasserstein distance-based ambiguity set offers strong theoretical properties and practical data utilization.
  • The discrepancy-based ambiguity set effectively estimates nominal distributions and reduces reliance on prior knowledge.
  • Experimental results in portfolio management showcase the advantages of the proposed EVaR-PC method.

Conclusions:

  • The novel EVaR-PC approximation provides a tractable and less conservative method for Robust Chance Constrained Optimization Problems (RCCOP).
  • The use of Wasserstein distance and discrepancy-based ambiguity sets enhances the practical applicability and data-driven nature of the optimization.
  • The method demonstrates significant advantages in applications like portfolio management, offering improved decision-making under uncertainty.