Related papers: On the continuous and smooth fit principle for opt…
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 consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
We consider an optimal liquidation problem with infinite horizon in the Almgren-Chriss framework, where the unaffected asset price follows a Levy process. The temporary price impact is described by a general function which satisfies some…
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…
As is well known, average-cost optimality inequalities imply the existence of stationary optimal policies for Markov Decision Processes with average costs per unit time, and these inequalities hold under broad natural conditions. This paper…
In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we…
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…
The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of…
In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to…
In this work the synthesis of approximate optimal and smooth feedback laws for infinite horizon optimal control problems is addressed. In this regards, $L^{p}$ type error bounds of the approximating smooth feedback laws are derived,…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
We consider the optimal stopping problem $v^{(\eps)}:=\sup_{\tau\in\mathcal{T}_{0,T}}\mathbb{E}B_{(\tau-\eps)^+}$ posed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov…
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 present an explicit solution to the Skorokhod embedding problem for spectrally negative L\'evy processes. Given a process $X$ and a target measure $\mu$ satisfying an explicit admissibility condition we define functions $\f_\pm$ such…
This article treats long term average impulse control problems with running costs in the case that the underlying process is a L\'evy process. Under quite general conditions we characterize the value of the control problem as the value of a…
We consider the optimal control problem associated with a general version of the well known shallow lake model, and we prove the existence of an optimum in the class $L_{loc}^{1}\left(0,+\infty\right)$. Any direct proof seems to be missing…
We study a mathematical model motivated by the support/resistance line method in technical analysis where the underlying stock price transitions between three states of nature in a path-dependent manner. For optimal stopping problems with…
We study the optimal multiple stopping time problem defined for each stopping time $S$ by $v(S)=\operatorname {ess}\sup_{\tau_1,...,\tau_d\geq S}E[\psi(\tau_1,...,\tau_d)|\mathcal{F}_S]$. The key point is the construction of a new reward…
The problem of optimal stopping with finite horizon in discrete time is considered in view of maximizing the expected gain. The algorithm proposed in this paper is completely nonparametric in the sense that it uses observed data from the…
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…