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Engineered and infrastructure systems deteriorate (e.g., loss capacity) as a result of adverse environmental or external conditions. Modeling deterioration is essential to define optimum design strategies and inspection and maintenance…

This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…

We study a system that experiences damaging external shocks at stochastic intervals, continuous degradation, and self-healing. The motivation for such a system comes from real-life applications based on micro-electro-mechanical systems…

We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we…

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded…

We study a single risky financial asset model subject to price impact and transaction cost over an finite time horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in…

We study a single risky financial asset model subject to price impact and transaction cost over an infinite horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in fixed…

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…

This paper deals with the assessment of the performance of a system under a finite planning horizon. The system is subject to two dependent causes of failure: internal degradation and sudden shocks. We assume that internal degradation…

This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…

In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second…

We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky…

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of…

We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…

This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…

Production systems deteriorate stochastically due to usage and may eventually break down, resulting in high maintenance costs at scheduled maintenance moments. This deterioration behavior is affected by the system's production rate. While…

In this paper, a condition-based imperfect maintenance model based on piecewise deterministic Markov process (PDMP) is constructed. The degradation of the system includes two types: natural degradation and random shocks. The natural…

We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…

We analyze an optimal control problem governed by a rate-independent system in an abstract infinite-dimensional setting. The rate-independent system is characterized by a nonconvex stored energy functional, which depends on time via a…