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Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…
In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…
In this paper, we study the optimal control system driven by stochastic differential equations (SDEs) of mean-field type, in which the control variable has two components, the first being absolutely continuous and the second singular. On…
In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a…
We prove a version of the stochastic maximum principle, in the sense of Pontryagin, for the finite horizon optimal control of a stochastic partial differential equation driven by an infinite dimensional additive noise. In particular we…
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux…
In this article, we present a general methodology for control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this…
The objective of this paper is to weaken the Lipschitz condition to a monotonicity condition and to study the corresponding Pontryagin stochastic maximum principle (SMP) for a mean-field optimal control problem under monotonicity…
In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk…
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by…
In this article we consider a stochastic optimal control problem where the dynamics of the state process, $X(t)$, is a controlled stochastic differential equation with jumps, delay and \emph{noisy memory}. The term noisy memory is, to the…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
Many natural systems exhibit phase transition where external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the behavior of a stochastic dynamic system such as the most probable…
We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…
We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric…
In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equations with pointwise delay in the state and with control dependent noise, in the general case of…
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order necessary conditions of optimality. A stochastic Pontryagin…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
In this paper, we study a class of stochastic optimal control problem with jumps under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic…