Related papers: Non linear optimal stopping problem and Reflected …
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
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…
Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations…
We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
In this paper we focus on the so called identification problem for a backward SDE driven by a continuous local martingale and a possibly non quasi-left-continuous random measure. Supposing that a solution (Y, Z, U) of a backward SDE is such…
In this short note we consider RBSDE with Lipschitz drivers and barrier processes that are optional and right upper semicontinuous. We treat the case when the barrier can be represented as a decreasing limit of cadlag barriers. We combine…
This paper establishes a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs for short). We prove the existence and uniqueness of the weak solution to RBSPDEs allowing for non-zero…
We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative…
We consider partial differential equations (PDEs) characterized by an upper barrier that depends on the solution itself and a fixed lower barrier, while accommodating a non-local driver. First, we show a Feynman-Kac representation for the…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show…
In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs, for short) where the generators, the terminal values and the barriers are all switched with positive…
We consider systems of backward stochastic differential equations with c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an increasing continuous function $H$. Our equations are defined on general probability spaces…
We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value…
In this article we study and classify optimal martingales in the dual formulation of optimal stopping problems. In this respect we distinguish between weakly optimal and surely optimal martingales. It is shown that the family of weakly…
In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…