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While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this…
We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion and the gain function is time-homogeneous and difference of two convex functions.…
We consider a reflected process in the positive orthant driven by an exogenous jump process. For a given input process, we show that there exists a unique minimal strong solution to the given particle system up until a certain maximal…
We propose a novel group of Gaussian Process based algorithms for fast approximate optimal stopping of time series with specific applications to financial markets. We show that structural properties commonly exhibited by financial time…
We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
Our purpose is to study a particular class of optimal stopping problems for Markov processes. We justify the value function convexity and we deduce that there exists a boundary function such that the smallest optimal stopping time is the…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. Our…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
In this paper, the stochastic verification theorems for stochastic control problems of reflected forward-backward stochastic differential equations are studied. We carry out the work within the frameworks of classical and viscosity…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the…
We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also covers the McKean-Vlasov case. Differently from what is usually…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
We present a method to solve optimal stopping problems in infinite horizon for a L\'evy process when the reward function can be non-monotone. To solve the problem we introduce two new objects. Firstly, we define a random variable $\eta(x)$…