Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications
By Huyen Pham. 2016
77 citations recorded by the source corpus.
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weighting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are introduced, and following the dynamic programming approach in (Pham and Wei, Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics, 2016), we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations. We present several financial applications with explicit solutions, and revisit, in particular, optimal tracking problems with price impact, and the conditional mean-variance portfolio selection in an incomplete market model.
Subfields: Finance
View Paper: https://www.semanticscholar.org/paper/5008e543a2c4a5c8b94a88ba831f06222a33d0ac
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Citations in the corpus
- McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “Specialisations to linear–quadratic settings were also explored by Pham [65], Li, Sun, and Yong [57], Li, Sun, and Xiong [58], Huang, Li, and Yong [43], Yong [80], and Basei and Pham [8].”
- Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, unknown): “Pham, H.: Linear quadratic optimal control of conditional McKean–Vlasov equation with random coefficients and applications.”
- Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, background): “Pham and Wei develop a dynamic programming technique (see also [49]), with corresponding Hamilton-Jacobi equations on an infinite dimensional space of probability measures, for solving mean field type optimal control problems, first without [56] and then with common noise [57].”