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In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control…
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…
In this paper, the problem of smart grid energy management under stochastic dynamics is investigated. In the considered model, at the demand side, it is assumed that customers can act as prosumers who own renewable energy sources and can…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
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…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
This paper analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary…
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…
We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…
In this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…
Time-consistency is an essential requirement in risk sensitive optimal control problems to make rational decisions. An optimization problem is time consistent if its solution policy does not depend on the time sequence of solving the…
In decision-dependent games, multiple players optimize their decisions under a data distribution that shifts with their joint actions, creating complex dynamics in applications like market pricing. A practical consequence of these dynamics…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in…
This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study…