相关论文: A simple model on streamflow management with a dyn…

In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…

We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…

We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…

We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learning rate, a general formula for computing the difference…

This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…

We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…

We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…

Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we…

We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the…

We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…

This paper shows how the theory of dynamic risk measures provides viscosity solutions to a family of second-order parabolic partial differential equations, even in the degenerate case. First, motivated by the martingale problem approach of…

We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…

Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…

The combination of boundary flow control and variable speed limit (VSL) is a widely used strategy for highway corridors to maintain safety and throughput when the capacity downstream is dropped. However, most proposed models assume fixed…

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…