Related papers: Regularity of the Optimal Stopping Problem for Jum…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
We study the problem of optimal stopping of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability…
We study the existence theory for parabolic variational inequalities in weighted $L^2$ spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for…
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…
Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent…
We study the ergodic control problem for a class of jump diffusions in $\mathbb{R}^d$, which are controlled through the drift with bounded controls. The Levy measure is finite, but has no particular structure; it can be anisotropic and…
In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
We present an analytic solution of a differential-difference equation that appears when one solves an optimal stopping time problem with state process following a jump-diffusion process. This equation occurs in the context of real options…
We study the optimal stopping problem for a monotonous dynamic risk measure induced by a BSDE with jumps in the Markovian case. We show that the value function is a viscosity solution of an obstacle problem for a partial…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and…
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],…
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…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…