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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…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
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 present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor's preferences are represented by a multivariate utility function, allowing for…
We consider a risk-sensitive optimization of consumption-utility on infinite time horizon where the one-period investment gain depends on an underlying economic state whose evolution over time is assumed to be described by a discrete-time,…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…
Adaptive optimal control using value iteration (VI) initiated from a stabilizing policy is theoretically analyzed in various aspects including the continuity of the result, the stability of the system operated using any single/constant…
In this paper, we consider the stochastic optimal control problem for a generalized Volterra control system. The corresponding state process is a kind of a generalized stochastic Volterra integral differential equations. We prove the…
We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
Deterministic optimal impulse control problem with terminal state constraint is considered. Due to the appearance of the terminal state constraint, the value function might be discontinuous in general. The main contribution of this paper is…
We consider "time-of-use" pricing as a technique for matching supply and demand of temporal resources with the goal of maximizing social welfare. Relevant examples include energy, computing resources on a cloud computing platform, and…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that…