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Impulse Control of Conditional McKean–Vlasov Jump Diffusions
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- Agram, Nacira, Associate professor, 1987- (author)
- KTH,Matematisk statistik
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- Pucci, Giulia (author)
- KTH,Matematisk statistik
- Øksendal, Bernt (author)
- (creator_code:org_t)
- Springer Nature, 2024
- 2024
- English.
- In: Journal of Optimization Theory and Applications. - : Springer Nature. - 0022-3239 .- 1573-2878. ; 200:3, s. 1100-1130
- Journal article (peer-reviewed)
Abstract
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- In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (subject category)
- art (subject category)
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