Related papers: Constructing Time-Homogeneous Generalised Diffusio…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game…
Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
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…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
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…
This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled…
In a classical problem for the stopping of a diffusion process $(X_t)_{t \geq 0}$, where the goal is to maximise the expected discounted value of a function of the stopped process ${\mathbb E}^x[e^{-\beta \tau}g(X_\tau)]$, maximisation…
This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…
This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the…