Related papers: Root's barrier: Construction, optimality and appli…
The conformal Skorokhod embedding problem (CSEP) is a planar variant of the classical problem where the solution is now a simply connected domain $D\subset\mathbb{C}$ whose exit time embeds a given probability distribution $\mu$ by…
In large-scale time series forecasting, one often encounters the situation where the temporal patterns of time series, while drifting over time, differ from one another in the same dataset. In this paper, we provably show under such…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and…
This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about…
We consider a toy model of rate independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We introduce a notion of solutions based on an obstacle problem. These solutions…
We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
We propose to learn the time-varying stochastic computational resource usage of software as a graph structured Schr\"odinger bridge problem. In general, learning the computational resource usage from data is challenging because resources…
We consider the problem of optimally stopping a Brownian bridge with an unknown pinning time so as to maximise the value of the process upon stopping. Adopting a Bayesian approach, we assume the stopper has a general continuous prior and is…
Recently, \cite{BeJu16, BeNuTo16} established that optimizers to the martingale optimal transport problem (MOT) are concentrated on $c$-monotone sets. In this article we characterize monotonicity preserving transformations revealing certain…
In the early 1930's, Erwin Schroedinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles. He showed that the solution to the problem…
In this paper, we revisit \textsf{ROOT-SGD}, an innovative method for stochastic optimization to bridge the gap between stochastic optimization and statistical efficiency. The proposed method enhances the performance and reliability of…
We consider a reflected backward stochastic differential equations with default time and an optional barrier in a filtration generated by a one-dimensional Brownian motion and a defaultable process. We suppose that the barrier have…
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…
The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…
This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…