Related papers: Global $C^1$ Regularity of the Value Function in O…
The optimal stopping problem for a Hunt processes on $\R$ is considered via the representation theory of excessive functions. In particular, we focus on infinite horizon (or perpetual) problems with one-sided structure, that is, there…
In this paper we prove local gradient estimates and higher differentiability result for the solutions of variational obstacle inequalities \int_\Omega\big<\mathcal{A}(x,u,Du),D(\phi-u)\big>dx\geq \int_\Omega\mathcal{B}(x,u,Du)(\phi-u)dx.…
We study the obstacle problem for parabolic operators of the type $\partial_t + L$, where $L$ is an elliptic integro-differential operator of order $2s$, such as $(-\Delta)^s$, in the supercritical regime $s \in (0,{1/2})$. The best result…
In the first part of this paper, we study RBSDEs in the case where the filtration is not quasi-left continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal…
We define a class of reflected backward stochastic differential equation (RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the solution is constrained to stay above a given c\`adl\`ag process. The MPP is only…
We study the higher regularity of free boundaries in obstacle problems for integro-differential operators. Our main result establishes that, once free boundaries are $C^{1,\alpha}$, then they are $C^\infty$. This completes the study of…
In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…
We analyze an irreversible investment decision for a project which yields a flow of future operating profits given by a geometric Brownian motion with unknown drift. In contrast to similar optimal stopping problems with incomplete…
A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
In this paper the Green formula for the operator of fractional differentiation in Caputo sense is proved. By using this formula the integral representation of all regular in a rectangular domains solutions is obtained in the form of the…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…
It's proved that a function connected with the Green function of the even order symmetric focal boundary value problem takes its maximal value on the diagonal.
We study the regularity of the solutions of second order boundary value problems on manifolds with boundary and bounded geometry. We first show that the regularity property of a given boundary value problem $(P, C)$ is equivalent to the…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…
We revisit the inverted pendulum problem with the goal of understanding and computing the true optimal value function. We start with an observation that the true optimal value function must be nonsmooth ($i.e.$, not globally $C^1$) due to…
We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…