arXiv research

Solves optimal stopping problem with Poisson constraints using jumps.

New algorithm solves complex stopping problems with robust optimization.

The paper tackles optimal stopping problems using reinforcement learning and singular control.

Dual martingales improve primal optimal stopping problem efficiency.

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …

Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.

DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.

In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem is well posed, in the sense that the value is indeed the unique …

MUSE provides unbiased stopping estimates for optimal problems.

Paper solves a complex stopping problem using regularization and HJB equations.

This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit …

Study on randomized algorithms for optimal stopping problems.

Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an opt…

Deep neural networks can solve optimal stopping problems without dimensionality issues.

New method solves optimal stopping problems using rough path signatures.

Develops a method for solving optimal stopping problems with multiple exercise rights.

Study optimal stopping times for multi-dimensional processes with non-exponential discounting.

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…

We consider the optimal double stopping time problem defined for each stopping time $S$ by $v(S)=\esssup\{E[ψ(τ_1, τ_2) | \F_S], τ_1, τ_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of …

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 ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary o…

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The op…

Early stopping method saves up to 75% computation time in policy search tasks.

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

A new method uses deep learning for optimal stopping problems.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to cons…

Probabilistic proof of smooth boundaries in optimal stopping problems.

We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of some continuous index process at which the payoff process is even allowed to have…

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated…

This paper considers a time-inconsistent stopping problem in which the inconsistency arises from non-constant time preference rates. We show that the smooth pasting principle, the main approach that has been used to construct explicit solutions for conventional time-consistent optimal stopping problems, may fail under …

Solves optimal stopping for Gauss-Markov bridges using time-space transformation.

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 a finite sequence of state-constrained optimal control problems with additional…

Improved algorithm for optimal stopping problems reduces runtime.

A new method solves complex financial problems using deep learning.

Improved reinforcement learning with emergency stops.

In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct $ε$-optimal stopping tim…

In this paper we study the problem of stopping a Brownian bridge $X$ in order to maximise the expected value of an exponential gain function. In particular, we solve the stopping problem $\sup_{0\le τ\le 1}\mathsf{E}[\mathrm{e}^{X_τ}]$ which was posed by Ernst and Shepp in their paper [Commun. Stoch. Anal., 9 (3), 20…

The paper tackles ICU discharge strategies by evaluating optimal stopping scenarios.

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $δ$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…

We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type.

We present a solution to an optimal stopping problem for a process with a wide-class of novel dynamics. The dynamics model the support/resistance line concept from financial technical analysis.

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

Study optimal timing to divest from assets with uncertain future scenarios.

The paper analyzes early stopping in linear regression and shows it's equivalent to ridge regularization.

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 regime-switching models. In this article, we reduce an optimal stopping problem with …

Investment strategy optimization from discrete to continuous models.

The research proposes a stopping rule for reinforcement learning algorithms based on instance-dependent confidence.

Study optimal stopping for diffusion processes with unknown primitives, applying RL and martingale methods.

Derives a new formula for optimal stopping problems with exploding derivatives.