Related papers: A Note on $G$- Optimal Stopping Problems
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
The purpose of this article is to study a stochastic control problem on a junction, with control at the junction point. The problem of control is formulated in the weak sense, using a relaxed control, namely a control which takes values in…
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…
Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…
We present a novel method for solving a class of time-inconsistent optimal stopping problems by reducing them to a family of standard stochastic optimal control problems. In particular, we convert an optimal stopping problem with a…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We…
In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…
We consider a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. More specifically, we set the absorbing boundary as S-b where b is a certain constant. This problem is…
We consider a class of infinite-time horizon optimal stopping problems for spectrally negative Levy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…