Related papers: Optimal Stopping under Nonlinear Expectation
We address an optimal stopping problem over the set of Bermudan-type strategies $\Theta$ (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time.…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
Let $\mathbb{\hat{E}}$ be the upper expectation of a weakly compact but non-dominated family $\mathcal{P}$ of probability measures. Assume that $Y$ is a $d$-dimensional $\mathcal{P}$-semimartingale under $\mathbb{\hat{E}}$. Given an open…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
Confidence sequences, anytime p-values (called p-processes in this paper), and e-processes all enable sequential inference for composite and nonparametric classes of distributions at arbitrary stopping times. Examining the literature, one…
This paper aims to address the nonlinear optimal guidance problem with impact-time and impact-angle constraints, which is fundamentally important for multiple pursuers to collaboratively achieve a target. Addressing such a guidance problem…
We consider the optimal prediction problem of stopping a spectrally negative L\'evy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions,…
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…
A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of…
We consider an optimal switching problem with random lag and possibility of component failure. The random lag is modeled by letting the operation mode follow a regime switching Markov-model with transition intensities that depend on the…
Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nano-scale system from one equilibrium state to another in finite time, Schmiedl and Seifert ({\it Phys. Rev. Lett.} {\bf 98},…
We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of $N$ items…