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We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a…
We present an information theoretic approach to stochastic optimal control problems that can be used to derive general sampling based optimization schemes. This new mathematical method is used to develop a sampling based model predictive…
We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian…
We consider the Merton problem of optimizing expected power utility of terminal wealth in the case of an unobservable Markov-modulated drift. What makes the model special is that the agent is allowed to purchase costly expert opinions of…
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 a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…
We address microscopic, agent based, and macroscopic, stochastic, modeling of the financial markets combining it with the exogenous noise. The interplay between the endogenous dynamics of agents and the exogenous noise is the primary…
Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…
This paper is devoted to an optimal control problem of fully coupled forward-backward stochastic differential equations driven by sub-diffusion, whose solutions are not Markov processes. The stochastic maximum principle is obtained, where…
This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…
Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads…
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…
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an It\^{o} process (the price process), and another non-homogeneous diffusion process (the exogenous…
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…
We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to exogenous stochastic demand. Each producer…
This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a…
In this paper, the formation control of multi-agent systems in random switching communication topology is studied, and the problem of excessive bandwidth and low control efficiency among multi-agents is solved. For nonlinear multi-agent…
We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movement. We apply this framework to the multi-intersection traffic light control…