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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:UNIVERSITY OF CENTRAL FLORIDA BOARD OF TRUSTEES, THE
Doing Business As Name:The University of Central Florida Board of Trustees
PD/PI:
  • Christian Keller
  • (213) 400-0656
  • christian.keller@ucf.edu
Award Date:07/28/2021
Estimated Total Award Amount: $ 133,000
Funds Obligated to Date: $ 133,000
  • FY 2021=$133,000
Start Date:09/01/2021
End Date:08/31/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Path-Dependent Partial Differential Equations and Optimal Control
Federal Award ID Number:2106077
DUNS ID:150805653
Parent DUNS ID:159621697
Program:APPLIED MATHEMATICS
Program Officer:
  • Eun Heui Kim
  • (703) 292-2091
  • eukim@nsf.gov

Awardee Location

Street:4000 CNTRL FLORIDA BLVD
City:Orlando
State:FL
ZIP:32816-8005
County:Orlando
Country:US
Awardee Cong. District:07

Primary Place of Performance

Organization Name:The University of Central Florida Board of Trustees
Street:4393 Andromeda Loop N
City:Orlando
State:FL
ZIP:32816-8007
County:Orlando
Country:US
Cong. District:07

Abstract at Time of Award

This research will advance optimal control theory to understand realistic and complex scenarios in applications. The research will potentially provide better or even optimal decision-making procedures, especially relevant for problems that affect many stakeholders such as pension fund investments and financial risk management. The project will provide training opportunities for graduate students and opportunities for STEM students to build their careers in the financial industry. The project consists of three parts. In the first part, the investigator will study optimal control problems involving non-Markovian piecewise deterministic processes and the associated non-local Hamilton-Jacobi-Bellman equations. Applications are optimal execution or liquidation problems in mathematical finance with richer classes of models. For example, non-Markovian Hawkes processes can be incorporated. Those processes provide a more accurate description of the relevant financial data. The second part deals with path-dependent Hamilton-Jacobi equations whose Hamiltonians can have quadratic or even super-quadratic growth in the gradient. Those equations are important for optimal control problems with unbounded controls. The investigator will develop new notions of non-smooth solutions and establish well-posedness results with respect to those notions. In the third part of this project, the investigator will completely carry out a path-dependent dynamic programming approach for the optimal control of locally monotone evolution equations. This large class of equations covers the two-dimensional Navier-Stokes equations and the tamed three-dimensional Navier-Stokes equations. In addition, this research provides a new line of methodologies for the largely open problem of optimal synthesis for infinite-dimensional control problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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