ﻻ يوجد ملخص باللغة العربية
We propose a new unbiased estimator for estimating the utility of the optimal stopping problem. The MUSE, short for `Multilevel Unbiased Stopping Estimator, constructs the unbiased Multilevel Monte Carlo (MLMC) estimator at every stage of the optimal stopping problem in a backward recursive way. In contrast to traditional sequential methods, the MUSE can be implemented in parallel when multiple processors are available. We prove the MUSE has finite variance, finite computational complexity, and achieves $varepsilon$-accuracy with $O(1/varepsilon^2)$ computational cost under mild conditions. We demonstrate MUSE empirically in several numerical examples, including an option pricing problem with high-dimensional inputs, which illustrates the use of the MUSE on computer clusters.
In this article we study and classify optimal martingales in the dual formulation of optimal stopping problems. In this respect we distinguish between weakly optimal and surely optimal martingales. It is shown that the family of weakly optimal and su
What type of delegation contract should be offered when facing a risk of the magnitude of the pandemic we are currently experiencing and how does the likelihood of an exogenous early termination of the relationship modify the terms of a full-commitme
This paper presents new machine learning approaches to approximate the solution of optimal stopping problems. The key idea of these methods is to use neural networks, where the hidden layers are generated randomly and only the last layer is trained,
We establish a generalization of Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton-Jacobi-Bellman equation associated to an opt
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance using th