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Climate change has a dramatic impact, particularly by concentrating rainfall into a few short periods, interspersed by long dry spells. In this context, the role of dams is crucial. We consider the optimal control of a dam, where the water…
The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). To this end, we first prove a stochastic…
We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the…
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…
In this paper, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
We study dynamics of the shearless stratified turbulent flows. Using the method of differential constraints we find a class of explicit solutions to the problem under consideration and establish that the differential constraint obtained…
Following the recent resurgence in establishing linear control theoretic benchmarks for reinforcement leaning (RL)-based policy optimization (PO) for complex dynamical systems with continuous state and action spaces, an optimal control…
We consider a class of diffusions controlled through the drift and jump size, and driven by a jump L\'evy process and a nondegenerate Wiener process, and we study infinite horizon (ergodic) risk-sensitive control problem for this model. We…
We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…