Integral equations for Rost’s reversed barriers: Existence and uniqueness results

Abstract

We establish that the boundaries of the so-called Rost's reversed barrier are the unique couple of left-continuous monotonic functions solving a suitable system of nonlinear integral equations of Volterra type. Our result holds for atom-less target distributions µ of the related Skorokhod embedding problem.The integral equations we obtain here generalise the ones often arising in optimal stopping literature and our proof of the uniqueness of the solution goes beyond the existing results in the field.MSC2010: 60G40, 60J65, 60J55, 35R35, 45D05.

From optimal stopping boundaries to Rost’s reversed barriers and the Skorokhod embedding

“…Remark 2.5. Under the additional assumption that µ is continuous we were able to prove in [12] that s ± uniquely solve a system of coupled integral equations of Volterra type and can therefore be evaluated numerically.…”

Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon

“…Optimal stopping with finite-time horizon paper: [34] addresses the question from a PDE point of view, [10] from a probabilistic one and [11] obtains the optimal boundaries numerically ( [8,Rem. 3.5] and [7,Rem.…”

Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon

“…An early contribution to optimal stopping theory fitting in our set-up is [24], which proposes a constructive procedure to identify the optimal boundary, based on PDE methods, under the requirement that the gain function be three times continuously differentiable. Stopping problems related to Röst's solution of the Skorokhod embedding problem are also covered by the present paper: [28] addresses the question from a PDE point of view, [9] from a probabilistic one and [10] obtains the optimal boundaries numerically ( [7,Rem. 3.5] and [6,Rem.…”