Related papers: Optimal stopping problems for the maximum process …
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
In the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including $(x^+)^{\nu}$, $(e^x-K)^+$, $(K-e^{-x})^+$,…
In this paper we study optimal stopping problems with respect to distorted expectations of the form \begin{eqnarray*} \mathcal{E}(X)=\int_{-\infty}^{\infty} x\,dG(F_X(x)), \end{eqnarray*} where $F_X$ is the distribution function of $X$ and…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
In this paper we study the problem of stopping a Brownian bridge $X$ in order to maximise the expected value of an exponential gain function. In particular, we solve the stopping problem $$\sup_{0\le \tau\le…
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…
In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…
Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is…
This paper attempts to study the optimal stopping time for semi-Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
Explicit solution of an infinite horizon optimal stopping problem for a Levy processes with a polynomial reward function is given, in terms of the overall supremum of the process, when the solution of the problem is one-sided. The results…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
We study an optimal process control problem with multiple assignable causes. The process is initially in-control but is subject to random transition to one of multiple out-of-control states due to assignable causes. The objective is to find…
This paper investigates optimal control problems for delayed systems governed by Infinitely Anticipated Backward Stochastic Differential Equations (IABSDEs). Unlike existing frameworks limited to bounded delays, we introduce a generalized…