Shahlar MeherremMokhtar HafayedDeniz Hasan GuçogluŞaban ErenHafayed, MokhtarMeherrem, ShahlarGucoglu, Deniz H.Eren, Saban2025-10-06201821952698, 2195268X2195-268X2195-269810.1007/s40435-017-0323-92-s2.0-85046782843https://www.scopus.com/inward/record.uri?eid=2-s2.0-85046782843&doi=10.1007%2Fs40435-017-0323-9&partnerID=40&md5=293fc6dd076beb1428a8c8311b82f6bbhttps://gcris.yasar.edu.tr/handle/123456789/9554https://doi.org/10.1007/s40435-017-0323-9In this paper a general characterization of the optimal stochastic combined control for mean-field jump-systems is derived by applying mixed convex-spike perturbation method. The diffusion coefficient depends on the continuous control variable and the control domain is not necessary convex. In our combined mean-field control problem we discuss two classes of jumps for the state processes the inaccessible jumps which caused by Poisson martingale measure and the predictable ones which caused by the singularity of the control variable. Markowitz’s mean–variance portfolio selection problem with intervention control is discussed. © 2020 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/closedAccessConvex-spike Perturbations, Markowitz’s Mean–variance Portfolio, Maximum Principle, Second-order Variational Equation, Singular Stochastic Control, Maximum Principle, Perturbation Techniques, Stochastic Control Systems, Continuous Control, Convex-spike Perturbations, Markowitz, Martingale Measures, Perturbation Method, Portfolio Selection Problems, Singular Stochastic Control, Variational Equations, Stochastic SystemsMaximum principle, Perturbation techniques, Stochastic control systems, Continuous control, Convex-spike perturbations, Markowitz, Martingale measures, Perturbation method, Portfolio selection problems, Singular stochastic control, Variational equations, Stochastic systemsSingular Stochastic ControlConvex-Spike PerturbationsSecond-Order Variational EquationMaximum PrincipleMarkowitz’s Mean–Variance PortfolioArticle