Related papers: Optimal Stopping under Model Ambiguity: a Time-Con…

We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we…

Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…

This paper characterizes differentiable and subgame Markov perfect equilibria in a continuous time intertemporal decision problem with non-constant discounting. Capturing the idea of non commitment by letting the commitment period being…

This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…

Standard selective prediction methods typically estimate uncertainty from the output of a single predictive branch. While effective for general uncertainty estimation, these approaches often struggle under partial observability, where local…

Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…

In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…

The absence of an algorithm that effectively monitors deep learning models used in side-channel attacks increases the difficulty of evaluation. If the attack is unsuccessful, the question is if we are dealing with a resistant implementation…

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional…

This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

Individuals use models to guide decisions, but many models are wrong. This paper studies which misspecified models are likely to persist when individuals also entertain alternative models. Consider an agent who uses her model to learn the…

Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate…

We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…

Sellers in online markets face the challenge of determining the right time to sell in view of uncertain future offers. Classical stopping theory assumes that sellers have full knowledge of the value distributions, and leverage this…

In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional…

In high-stakes applications, predictive models must not only produce accurate predictions but also quantify and communicate their uncertainty. Reject-option prediction addresses this by allowing the model to abstain when prediction…

This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…