Related papers: The non-linear multiple stopping problem: between …
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…
This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…
For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
In this work we study the optimal execution problem with multiplicative price impact in algorithm trading, when an agent holds an initial position of shares of a financial asset. The inter-selling-decision times are modelled by the arrival…
We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…
Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…
We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies…
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
In the multi-armed bandit framework, there are two formulations that are commonly employed to handle time-varying reward distributions: adversarial bandit and nonstationary bandit. Although their oracles, algorithms, and regret analysis…
In this paper we study a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero sum Stackelberg game between the principal and agent to a standard…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
We solve the binary decision model of Brock and Durlauf in time using a method reliant on the resolvent of the master operator of the stochastic process. Our solution is valid when not at equilibrium and can be used to exemplify…
This paper studies dynamic mechanism design in a quasilinear Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent's…