Related papers: Recombining Tree Approximations for Optimal Stoppi…
In this paper we introduce a numerical method for optimal stopping in the framework of one dimensional diffusion. We use the Skorokhod embedding in order to construct recombining tree approximations for diffusions with general coefficients.…
Given a Brownian motion $B_t$ and a general target law $\mu$ (not necessarily centered or even integrable) we show how to construct an embedding of $\mu$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…
We investigate quantifying the difference between two hybrid dynamical systems under noise and initial-state uncertainty. While the set of traces for these systems is infinite, it is possible to symbolically approximate trace sets using…
In this paper we consider the Skorokhod embedding problem for target distributions with non-zero mean. In the zero-mean case, uniform integrability provides a natural restriction on the class of embeddings, but this is no longer suitable…
We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions…
Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…
We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpreted in Skorohod sense. Although alternative proof techniques…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria…
We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0,\infty],…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion…
We investigate the optimal stopping problems involving the supremum of a diffusion. The starting point is the link between works of Peskir and Meilijson, which we describe in a unified manner. The description developped follows mainly the…
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a…
A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…
We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally…