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Bellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that the nonlinear term is positive quadratic form on first-order partial derivatives of solution, which includes linear exponential…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.…
This paper develops a quantized Q-learning algorithm for the optimal control of controlled diffusion processes on $\mathbb{R}^d$ under both discounted and ergodic (average) cost criteria. We first establish near-optimality of finite-state…
A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
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 investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontryagin's maximum principle and also invalidates the standard…
We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…
In this paper we consider ergodic optimal control of a diffusion process $\{X^u_t\}_{t \geq 0}$, taking values in $\bR^n$, where both drift and volatility are controlled. We establish a novel strong duality between the existence of a unique…
We consider a control problem for a heterogeneous population composed of agents able to switch at any time between different options. The controller aims to maximize an average gain per time unit, supposing that the population is of…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
In this article we study ergodic problems in the whole space $\mathbb{R}^N$ for weakly coupled systems of viscous Hamilton-Jacobi equations with coercive right-hand sides. The Hamiltonians are assumed to have a fairly general structure and…
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…
We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markov model. Two approaches are used to obtain the distribution. The…
This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…