Related papers: Exact optimal stopping for multidimensional linear…
Among various rare events, the effective computation of transition paths connecting metastable states in a stochastic model is an important problem. This paper proposes a stochastic optimal control formulation for transition path problems…
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…
Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…
It is well known that stability is the most fundamental nature with regard to a control system, in view of this, the stabilization becomes an inevitable control problem. This article mainly discusses the optimal control and stabilization…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy…
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
We show that the optimal decision policy for several types of Bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions. This is established by using lattice programming and…
This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic. Our method is…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…
We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…