Journal ArticleDOI
Singular Stochastic Control, Linear Diffusions, and Optimal Stopping: A Class of Solvable Problems
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TLDR
It is demonstrated that given these conditions increased stochastic fluctuations decrease the value and increase the optimal threshold, thus postponing the exercise of the irreversible policy.Abstract:
We consider a class of singular stochastic control problems arising frequently in applications of stochastic control. We state a set of conditions under which the optimal policy and its value can be derived in terms of the minimal r-excessive functions of the controlled diffusion, and demonstrate that the optimal policy is of the standard local time type. We then state a set of weak smoothness conditions under which the value function is increasing and concave, and demonstrate that given these conditions increased stochastic fluctuations decrease the value and increase the optimal threshold, thus postponing the exercise of the irreversible policy. In line with previous studies of singular stochastic control, we also establish a connection between singular control and optimal stopping, and show that the marginal value of the singular control problem coincides with the value of the associated stopping problem whenever 0 is not a regular boundary for the controlled diffusion.read more
Citations
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Journal ArticleDOI
Controlled diffusion processes
TL;DR: In this article, the authors give an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions.
Journal ArticleDOI
Controlled diffusion processes
TL;DR: In this article, the authors give an overview of the developments in controlled============diffusion processes, emphasizing key results regarding existence and characterization of optimal controls and their characterization via dynamic======programming for a variety of cost criteria and structural assumptions.
Journal ArticleDOI
Optimal harvesting under resource stock and price uncertainty
Luis H. R. Alvarez,Erkki Koskela +1 more
TL;DR: In this article, the authors analyzed partial and complete depletion harvesting policy under resource stock and price uncertainty and risk neutrality, and showed that the value can be expressed in a separable form where price volatility affects the value through the risk adjusted growth rate.
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On the properties of $r$-excessive mappings for a class of diffusions
TL;DR: In this paper, the authors consider the convexity and comparative static properties of a class of $r$-harmonic mappings for a given linear, time-homogeneous and regular diffusion process.
Journal ArticleDOI
A Class of Solvable Impulse Control Problems
TL;DR: In this article, the authors consider a class of stochastic impulse control problems where the controlled process evolves according to a linear, regular, and time homogeneous diffusion and state a set of easily verifiable sufficient conditions under which the problem is explicitly solvable.
References
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Journal ArticleDOI
Stochastic differential equations : an introduction with applications
TL;DR: Some Mathematical Preliminaries as mentioned in this paper include the Ito Integrals, Ito Formula and the Martingale Representation Theorem, and Stochastic Differential Equations.
Book
Controlled Markov processes and viscosity solutions
Wendell H. Fleming,H. Mete Soner +1 more
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
Journal ArticleDOI
Mathematical Bioeconomics: The Optimal Management of Renewable Resources.
TL;DR: In this article, the authors present a model for renewable-resource harvesting based on the Schaefer model with a focus on the one-dimensional control problem and its application to policy problems.
Book
Mathematical bioeconomics: The optimal management of renewable resources
TL;DR: In this paper, the authors present a model for renewable-resource harvesting based on the Schaefer model with a focus on the one-dimensional control problem and its application to policy problems.
Book
Diffusion Processes and their Sample Paths
Kiyosi Itô,Henry P. McKean +1 more
TL;DR: In this article, the authors consider the problem of approximating the Brownian motion by a random walk with respect to the de Moivre-laplace limit theorem and show that it is NP-hard.