Related papers: Minimal Quantile Functions Subject to Stochastic D…
Stochastic gradient descent (SGD) has proven effective in solving many inventory control problems with demand learning. However, it often faces the pitfall of an infeasible target inventory level that is lower than the current inventory…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
The solution to a stochastic optimal control problem can be determined by computing the value function from a discretization of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a…
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic…
The minimal dominating Set (MDS) problem is a prototypical hard combinatorial optimization problem. Two years ago we studied this problem by cavity method. Although we get the solution of a given graph, which gives very good estimation of…
Motivated by the model- independent pricing of derivatives calibrated to the real market, we consider an optimization problem similar to the optimal Skorokhod embedding problem, where the embedded Brownian motion needs only to reproduce a…
This work contains two single-letter upper bounds on the entropy rate of a discrete-valued stationary stochastic process, which only depend on second-order statistics, and are primarily suitable for models which consist of relatively large…
The ${\alpha}$-quantile of a stochastic process $M_{t,{\alpha}}$ has been introduced in Miura (Hitotsubashi J Commerce Manag 27(1):15-28, 1992), and important distributional results have been derived in Akahori (Ann Appl Probab…
Processes controlled by stochastic synthesis and degradation (SSD) are widespread in biology but their reaction kinetics are not well understood. Using methods borrowed from the theory of resetting processes, we determine the first-passage…
We study the optimization of Steklov eigenvalues with respect to a boundary density function $\rho$ on a bounded Lipschitz domain $\Omega \subset \mathbb{R}^N$. We investigate the minimization and maximization of $\lambda_k(\rho)$, the…
Efficient optimization remains a fundamental challenge across numerous scientific and engineering domains, especially when objective function and gradient evaluations are computationally expensive. While zeroth-order optimization methods…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
In non-smooth stochastic optimization, we establish the non-convergence of the stochastic subgradient descent (SGD) to the critical points recently called active strict saddles by Davis and Drusvyatskiy. Such points lie on a manifold $M$…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss). Two types of FBS{\Delta}Ss are investigated. The first one is described by a partially…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential…
We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this…