相关论文: Risk-Sensitive Control and an Abstract Collatz-Wie…

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply to stabilize the interbank system with borrowing and lending activities. Facing both heterogeneity among banks and the common…

We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained…

In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of…

In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for…

We consider the stochastic Landau-Lifshitz-Bloch equation in dimensions 1,2,3, perturbed by a real-valued Wiener process. We consider a Suslin space-valued control process with a general control operator, which can depend on both the…

There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo…

In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^{1}$-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing…

In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic…

Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…

This paper explores the application of nonsmooth analysis in the Wasserstein space to finite-horizon optimal control problems for nonlocal continuity equations. We characterize the value function as a strict viscosity solution of the…

We introduce a novel extension to robust control theory that explicitly addresses uncertainty in the value function's gradient, a form of uncertainty endemic to applications like reinforcement learning where value functions are…

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…

The paper deals with the Dirac operator generated on the finite interval $[0,\pi]$ by the differential expression $-B\mathbf{y}'+Q(x)\mathbf{y}$, where $$ B=\begin{pmatrix}0&1\\-1&0\end{pmatrix},\qquad…

We derive a closed-form expression capturing the degree of Relative Risk Aversion (RRA) of investors for non-"fair" lotteries. We argue that our formula is superior to earlier methods that have been proposed, as it is a function of only…

An explicit construction is provided for embedding n positive eigenvalues in the spectrum of a Schroedinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type,…

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…

The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first exit time of…

We derive a feasible criterion for the bias-optimal selection of the tuning parameters involved in estimating the integrated volatility of the spot volatility via the simple realized estimator by Barndorff-Nielsen and Veraart (2009). Our…

In the past couple of decades, the use of ``non-quadratic" convex cost functions has revolutionized signal processing, machine learning, and statistics, allowing one to customize solutions to have desired structures and properties. However,…

This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…