Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures
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.
WOS:001166433804004
2023-01-01
979-8-3503-0124-3
New York
4836
4842
REVIEWED
Event name | Event place | Event date |
Singapore, SINGAPORE | DEC 13-15, 2023 | |
Funder | Grant Number |
NSF | CNS1646121 |
AFOSR | FA9550-19-10005 |
ONR | N00014-21-1-2431 |
Chateaubriand Fellowship of the Office for Science & Technology of the Embassy of France in the United States | |
Swiss National Science Foundation | 200021 178890 |
French company Reseau de Transport d' 'Electricite | |
Swiss National Science Foundation under the "NCCR Automation" | 51NF40 180545 |
Office for Science & Technology of the Embassy of France in the United States | |