Related papers: An optimal multibarrier strategy for a singular st…
In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular…
This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…
We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modelled by a linear diffusion. The control that can be…
We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is $C^1$ and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the…
We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…
We consider the problem of steering, via output feedback, the state distribution of a discrete-time, linear stochastic system from an initial Gaussian distribution to a terminal Gaussian distribution with prescribed mean and maximum…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
This paper studies the continuous-time reinforcement learning for stochastic singular control with the application to an infinite-horizon irreversible reinsurance problems. The singular control is equivalently characterized as a pair of…
We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e. the dividend rate can never decrease. We solve the resulting two-dimensional…
This paper studies a general L\'evy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in…
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 develop a model-free approach to optimally control stochastic, Markovian systems subject to a reach-avoid constraint. Specifically, the state trajectory must remain within a safe set while reaching a target set within a finite time…
Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…
We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…
We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…