Related papers: Constrained Optimal Stopping, Liquidity and Effort

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…

We introduce a novel extension of the canonical multi-armed bandit problem that incorporates an additional strategic innovation: abstention. In this enhanced framework, the agent is not only tasked with selecting an arm at each time step,…

We study the properties of the free boundaries and the corresponding hitting times in the context of optimal stopping in discrete time. We first prove the continuity of the map from the boundaries to the expected value of the corresponding…

We describe the solution of an optimal stopping problem for a stable L\'evy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains…

We consider the problem of designing a sequential decision making agent to maximize an unknown time-varying function which switches with time. At each step, the agent receives an observation of the function's value at a point decided by the…

A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time \tau the random walk reaches a given level. Specifically, the p-moment…

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…

We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on…

We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…

Sample size determination is crucial in experimental design, especially in traffic and transport research. Frequentist statistics require a fixed sample size determined by power analysis, which cannot be adjusted once the experiment starts.…

We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…

Originally motivated by default risk management applications, this paper investigates a novel problem, referred to as the profitable bandit problem here. At each step, an agent chooses a subset of the K possible actions. For each action…

We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…

Agents that learn to select optimal actions represent a prominent focus of the sequential decision-making literature. In the face of a complex environment or constraints on time and resources, however, aiming to synthesize such an optimal…

We consider a version of the continuum armed bandit where an action induces a filtered realisation of a non-homogeneous Poisson process. Point data in the filtered sample are then revealed to the decision-maker, whose reward is the total…

This note considers a variation of the full-information secretary problem where the random variables to be observed are independent and identically distributed. Consider $X_1,\dots,X_n$ to be an independent sequence of random variables, let…

In classic reinforcement learning algorithms, agents make decisions at discrete and fixed time intervals. The duration between decisions becomes a crucial hyperparameter, as setting it too short may increase the problem's difficulty by…

We introduce the problem of assigning resources to improve their utilization. The motivation comes from settings where agents have uncertainty about their own values for using a resource, and where it is in the interest of a group that…

This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be…

In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm, i.e. the amount…