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Communication Dans Un Congrès Année : 2024

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

Résumé

This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Value-at-Risk (VaR) of a state function along SDE state distributions. The VaR problem is upper-bounded by an infinite-dimensional Second-Order Cone Program in occupation measures through the use of one-sided Cantelli or Vysochanskii-Petunin inequalities. These upper bounds on the true quantile statistics may be approximated from above by a sequence of Semidefinite Programs in increasing size using the moment-Sum-of-Squares hierarchy when all data is polynomial. Effectiveness of this approach is demonstrated on example stochastic polynomial dynamical systems.
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Dates et versions

hal-04055180 , version 1 (01-04-2023)

Identifiants

Citer

Jared Miller, Matteo Tacchi, Mario Sznaier, Ashkan Jasour. Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures. CDC 2023 - 62nd IEEE Conference on Decision and Control, Dec 2023, Singapore, Singapore. pp.4836-4842, ⟨10.1109/CDC49753.2023.10383958⟩. ⟨hal-04055180⟩
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