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We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the optimal control theory. We present a necessary and…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
We consider the problem of reducing the carbon emissions of a set of firms over a finite horizon. A regulator dynamically allocates emission allowances to each firm. Firms face idiosyncratic as well as common economic shocks on emissions,…
We consider an optimal control problem for a linear stochastic integro-diffe\-rential equation with conic constraints on the phase variable and the control of singular-regular type. Our setting includes consumption-investment problems for…
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…
In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient constraint and a partial integro-differential operator whose L\'evy measure…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
This paper explores stochastic control models in the context of decarbonization within the energy market. We study three progressively complex scenarios: (1) a single firm operating with two technologies-one polluting and one clean,(2)two…
We investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontryagin's maximum principle and also invalidates the standard…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear…