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Repair mechanisms are important within resilient systems to maintain the system in an operational state after an error occurred. Usually, constraints on the repair mechanisms are imposed, e.g., concerning the time or resources required…
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…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. Specifically, we obtain the viscosity property of value functions, the uniqueness of viscosity solutions, the regularity of value…
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…
We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
Previous work has separately addressed different forms of action, state and action-state entropy regularization, pure exploration and space occupation. These problems have become extremely relevant for regularization, generalization,…
We consider a class of impulse control problems for general underlying strong Markov processes on the real line, which allows for an explicit solution. The optimal impulse times are shown to be of threshold type and the optimal threshold is…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk…