Related papers: Optimal Stopping under G-expectation

We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer.…

This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…

Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…

Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…

Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…

We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…

In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion…

We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…

We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as $Y$ by convention, but in terms of its conditional expectation…

We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…

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…

In this paper, we study the solvability of a class of multi-dimensional forward backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such…

This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random…

We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0,\infty],…

This paper characterizes the solution to a finite horizon min-max optimal control problem where the system is linear and discrete-time with control and state constraints, and the cost quadratic; the disturbance is negatively costed, as in…

We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval $(0,\, T)$ that depends on…

Given a spectrally negative L\'evy process $X$ drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the $L^p$ distance ($p>1$) with $g$, the last time $X$ is…

In this Note we study optimal stopping problems for strong Markov processes and affine functions. We give a justification of the Snell envelope form using standard results of optimal stopping. We also justify the convexity of the value…

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…