On partial-information optimal singular control problem for mean-field stochastic differential equations driven by Teugels martingales measures

Abstract

This paper is concerned with partial-information mixed optimal stochastic continuoussingular control problem for mean-field stochastic differential equation driven by Teugels martingales and an independent Brownian motion, where the Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes. The control variable has two components; the first being absolutely continuous, and the second singular. Partial-information necessary and sufficient conditions of optimal continuous-singular control for these mean-field models are investigated. As an illustration, this paper studies a partial-information linear quadratic control problem of mean-field type involving continuous-singular control.

An optimal control problem for linear SDE of mean-field type with terminal constraint and partial information

“…The control problem is also related to those of Meyer-Brandis et al [10], Elliott et al [11], Yong [12], Hafayed and Abbas [13], Ni et al [14] and Hafayed et al [15]. Specifically, [10,15], respectively, studied a mean-field type control problem with partial information, where neither noisy observation nor filter is studied. The other work investigated meanfield type controls with complete information.…”

On optimal solutions of general continuous‐singular stochastic control problem of McKean‐Vlasov type

“…Optimal control problems for McKean‐Vlasov‐type stochastic differential equations (SDEs) have been studied by many authors; see, for example, previous studies. Peng's type necessary conditions in the form of maximum principle for SDEs of mean‐field type have proved by Buckdahn et al The necessary optimality conditions for SDEs have been established by Wang et al Stochastic optimal control of mean‐field jump‐diffusion systems with delay has been studied by Meng and Shen . The necessary and sufficient conditions for mean‐field SDEs governed by Teugels martingales associated to Lévy process have been studied in previous studies .…”

“…Necessary conditions for optimal stochastic singular control have been investigated by many authors, see for instance previous studies . Necessary conditions for optimal singular stochastic control systems with variable delay have been studied in Aghayeva and Morali .…”

On optimal singular control problem for general Mckean‐Vlasov differential equations: Necessary and sufficient optimality conditions

“…General necessary and sufficient conditions of the optimality and near‐optimality for the continuous‐singular control for the mean‐field SDE have been established in the work of Hafayed and Abbas . Under partial information, necessary and sufficient conditions for the optimal control for stochastic systems driven by Lévy processes have been derived by Hafayed et al The maximum principle for the optimal singular control of mean‐field stochastic systems governed by Lévy processes, associated with Teugels martingales measures, has been investigated by Hafayed et al Necessary and sufficient conditions of the optimality for the singular control of the mean‐field forward‐backward stochastic systems have been derived by Hafayed . A McKean‐Vlasov optimal mixed regular‐singular control problems for nonlinear stochastic systems with Poisson jump processes have been studied in the work of Hafayed et al A Peng's‐type maximum principle for SDEs of the mean‐field type, in which the coefficients depend on the state of the solution process and of its expected value, was investigated in the work of Buckdahn et al Sufficient conditions for the optimal control of mean‐field SDEs have been obtained by Shi .…”

“…The stochastic control problems for the mean-field system type, where the coefficients depend on the state of the solution process and of its expected value, have been investigated by many authors. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] The stochastic maximum principle for the optimal control of mean-field stochastic differential equations (SDEs), under partial information, has been investigated in the work of Wang et al 3 The maximum principle for mean-field-type SDEs with correlated state and observation noises has been established in the work of Zhang. 4 The stochastic optimal control of mean-field jump-diffusion systems with delay has been studied by Meng and Shen.…”