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Stochastic Fokker-P...
Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control
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- Agram, Nacira, Associate professor, 1987- (författare)
- KTH,Matematisk statistik
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- Øksendal, Bernt (författare)
- Department of Mathematics, University of Oslo, Oslo, Norway
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(creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2023
- 2023
- Engelska.
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 61:3, s. 1472-1493
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffu-sions, for short). To this end, we first prove a stochastic Fokker-Planck equation for the conditional law of the solution of such equations. Combining this equation with the original state equation, we obtain a Markovian system for the state and its conditional law. Furthermore, we apply this to formulate a Hamilton-Jacobi-Bellman equation for the optimal control of conditional McKean-Vlasov jump diffusions. Then we study the situation when the law is absolutely continuous with respect to Lebesgue measure. In that case the Fokker-Planck equation reduces to a stochastic par-tial differential equation for the Radon-Nikodym derivative of the conditional law. Finally we apply these results to solve explicitly the linear-quadratic optimal control problem of conditional stochastic McKean-Vlasov jump diffusions, and optimal consumption from a cash flow.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- jump diffusion
- common noise
- conditional McKean-Vlasov differential equation
- stochastic Fokker-Planck equation
- optimal control
- HJB equation
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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