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We provide a new probabilistic proof of the connection between Rost's solution of the Skorokhod embedding problem and a suitable family of optimal stopping problems for Brownian motion with finite time-horizon. In particular we use…
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.
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…
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 deal with Skorokhod problem for right continuous left limited (rcll) barriers. We prove existence and uniqueness of the solution when the barriers are only supposed to be rcll and completely separated. Then, we apply our…
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…
We consider reflected backward stochastic differential equations with two optional barriers of class (D) satisfying Mokobodzki's separation condition and coefficient which is only continuous and non-increasing. We assume that data are…
We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we…
In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a…
This paper contains a study on stochastic Volterra integral equations with fuzzy sets-values and involving on a constant retardation. Moreover, the form of the equation is symmetric in the sense that fuzzy stochastic integrals are placed on…
We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the…
In this paper, we study a kind of constrained backward stochastic differential equations (BSDEs) such that the nonlinear expectation of the composition of a loss function and the solution remains above zero. The existence and uniqueness…
The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…
We derive a nonlinear integral equation to calculate Root's solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate bounded time-space increments of Brownian motion and give a…
We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of…
The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is…
In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a…
In this paper we present some new results regarding the solvability of nonlinear Hammerstein integral equations in a special cone of continuous functions. The proofs are based on a certain fixed point theorem of Leggett and Williams type.…
We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove…
We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…