Related papers: Monte Carlo methods via a dual approach for some d…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-hard due to the binary constraints. We develop a novel…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We…
Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
We derive an algorithm in the spirit of Rogers and Davis & Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in the work of Guyon & Henry-Labord\`ere. We…
Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries.…
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
This study addresses the difficulties associated with inventory management of products with stochastic demand. The objective is to find the optimal combination of order quantity and reorder point that maximizes profit while considering…
Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
Safety evaluation of self-driving technologies has been extensively studied. One recent approach uses Monte Carlo based evaluation to estimate the occurrence probabilities of safety-critical events as safety measures. These Monte Carlo…
We introduce and develop a novel particle exchange Monte Carlo method. Whereas existing methods apply to eigenfunction problems where the eigenvalue is known (e.g., integrals with respect to a Gibbs measure, which can be interpreted as…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing,…