Related papers: Reflected stochastic recursive control problems wi…
In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…
Throughout this paper, we focused our aim on the problem of optimal control under a risk-sensitive performance functional, where the system is given by a fully coupled forward-backward stochastic differential equation with jump. The risk…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is…
In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state $Y^{u}$ is multiplicatively influenced by an unknown random variable…
In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…
This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub-…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…
We consider Neumann problem for linear elliptic equations involving integro-differential operators of Levy-type. We show that suitably defined viscosity solutions have probabilistic representations given in terms of the reflected stochastic…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of 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…