Related papers: The Skorokhod embedding problem and its offspring
This paper examines the Root solution of the Skorohod embedding problem given full marginals on some compact time interval. Our results are obtained by limiting arguments based on finitely-many marginals Root solution of Cox, Obl\'oj and…
We revisit work of Rost, Dupire and Cox--Wang on connections between Root's solution of the Skorokhod embedding problem and obstacle problems. We develop an approach based on viscosity sub- and supersolutions and an accompanying comparison…
In this paper, we study the Skorokhod problem with two constraints, where the constraints are in a nonlinear fashion. We prove the existence and uniqueness of the solution and also provide the explicit construction for the solution. In…
In this work, we investigate the problem of the boundedness of the Gross' solutions of the planar Skorokhod embedding problem, where we show that the solution is bounded under some mild conditions on the underlying probability distribution.
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…
We show that the barrier function in Root's solution to the Skorokhod embedding problem is continuous and finite at every point where the target measure has no atom and its absolutely continuous part is locally bounded away from zero.
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…
The planar Skorokhod embedding problem was first proposed and solved by R. Gross in 2019 [#gross2019]. Gross worked with probability distributions having finite second moment. In [#boudabra2019remarks, #Boudabra2020], the solutions extended…
We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal…
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval $[0,1]$. The problem is related to the study of extremal martingales associated with a peacock ("process increasing in convex order", by…
We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of Markovian excursions. Our setting allows to solve the Skorokhod embedding problem, in particular, for diffusions…
Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root's work shows that there exists a barrier…
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 report on various results, conjectures, and open problems related to Kazhdan-Lusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.
In this note we give a proof of the Sobolev and Morrey embedding theorems based on the representation of functions in terms of the fundamental solution of suitable partial differential operators. We also prove the compactness of the Sobolev…
Skorokhod problem arises in studying Reflected Brownian Motion (RBM) on an non-negative orthant, specifically in the context of queueing networks in the heavy traffic regime. One of the key problems is identifying conditions for stability…
In this paper, we provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established by Beiglb\"ock, Cox and Huesmann. This principle presents a geometric characterization that reflects the…
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
In this article, we consider a generalisation of the Skorokhod embedding problem (SEP) with a delayed starting time. In the delayed SEP, we look for stopping times which embed a given measure in a stochastic process, which occur after a…