Study perfect times to sell near asset peak in minimax setting.
problem Optimizing selling times for assets near their peak price.
method Introduces a unique selling rule based on price deviation from peak.
result Found optimal selling times that improve any earlier rule.
Study optimal stopping in non-exponential discounting, finding unique equilibrium.
problem Optimal stopping under non-exponential discounting.
method Iterative approach to find subgame perfect Nash equilibria.
result Existence and uniqueness of optimal equilibrium with higher value.
Study resolves time consistency in mean-standard deviation stopping problem for discrete time.
problem Time consistency in mean-standard deviation stopping problem for discrete time.
method Formulated as subgame perfect Nash equilibrium, considering liquidation strategies.
result Equilibrium liquidation strategy always exists, but optimal strategies may not.
Introduces strong equilibrium for time-inconsistent stopping problems in continuous time.
problem Time-inconsistent stopping problems in continuous time.
method Introduces strong equilibrium, compares with existing mild and weak equilibria, and provides an iteration method to construct optimal mild equilibria.
result Optimal mild equilibria are always strong equilibria under certain conditions.
New approach for optimal stopping under model ambiguity, considering agent's attitude towards ambiguity.
problem Optimal stopping under model ambiguity and varying levels of ambiguity aversion.
method Introduces a time-inconsistent stopping problem with an α-maxmin nonlinear expectation and seeks subgame perfect equilibrium policies through fixed-point iterations. result Equilibrium stopping policies can be obtained through fixed-point iteration and vary based on an agent's ambiguity attitude.
New conditions for GRW space-times to be perfect-fluid space-times.
problem Conditions for GRW space-times to be perfect-fluid.
method Gray's decomposition of the gradient of the Ricci tensor, determining Ricci tensor forms in invariant subspaces.
result For most GRW space-times, the Ricci tensor is Einstein or perfect fluid.
Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
Perfect fluids in higher dimensions become generalized Robertson-Walker spaces under specific conditions.
problem Characterizing perfect-fluid space-times as generalized Robertson-Walker spaces.
method Analyzing conditions for a perfect-fluid space-time to be a generalized Robertson-Walker space-time.
result Conditions for a perfect-fluid space-time to be a generalized Robertson-Walker space-time are verified.
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
Continuous-time optimal stopping solved with deep reinforcement learning
problem Optimal stopping problems in continuous time
method CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping)
result Higher prices than existing Bermudan solvers, approaching American upper bound
Discrete-time games reveal payoffs after both players stop, leading to new equilibrium strategies.
problem Non-zero-sum stopping games with delayed payoff revelation.
method Analyzes simultaneous and sequential stopping strategies, proving Nash equilibria in both cases.
result Existence of Nash equilibria in mixed and pure stopping strategies.
New algorithms improve stopping time for best arm identification.
problem Efficiently identifying the best alternative in experiments.
method Proposed algorithms with exponential-tailed stopping time.
result Proved that some algorithms never stop, leading to new methods.
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 …
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.
The paper shows failure of smooth pasting principle in time-inconsistent stopping problems.
problem Time-inconsistent stopping problems with non-constant time preference rates.
method Analysis of the smooth pasting principle within the intra-personal game theoretic framework.
result The smooth pasting principle fails under time-inconsistency and does not guarantee equilibrium solutions.
New findings on GRW space-times with constant scalar curvature.
problem Understanding GRW space-times in different subspaces.
method Analyzing orthogonal subspaces of Gray's decomposition.
result Generalized quasi-Einstein GRW space-times reduce to known types of space-times.
We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
New approach to optimal stopping under bounded rationality, considering future events.
problem Optimal stopping with conditional objectives, e.g., survival or non-bankruptcy.
method Equilibrium approach for time-inconsistent optimization, generalizing Snell envelope.
result Equilibria are unique in finite time but non-uniqueness in infinite time.
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…
The paper tackles optimal stopping problems using reinforcement learning and singular control.
problem Continuous-time and state-space optimal stopping problems.
method Formulated as a singular control problem with randomized stopping times and penalized cumulative residual entropy.
result Identified unique optimal exploratory strategy through dynamic programming.
In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.
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 …
Early stopping method saves up to 75% computation time in policy search tasks.
problem Lengthy evaluation times in optimization problems, especially in robotics.
method A generalized early stopping criterion that only uses objective value at each time step.
result The method saves up to 75% computation time compared to no stopping.
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Method calculates Parisian stopping times and option prices using Markov chains.
problem Computing distribution and pricing of Parisian stopping times under Markov processes.
method Continuous-time Markov chain approximation to solve for distribution and convergence analysis.
result Sharp convergence rate and efficient method for diffusion and jump models.
Optimal stopping times maximize/minimize Brownian motion distance between radially symmetric marginals.
problem Optimal stopping times for Brownian motion between radially symmetric marginals.
method Characterization through Skorohod embeddings and optimal mass transport with subharmonic constraints.
result Optimal stopping times are hitting times of suitable barriers, non-randomized, and unique under radial symmetry.
Study optimal stopping times under regime-switching models with constraints.
problem Optimal stopping times for discounted payoffs on a regime-switching geometric Brownian motion.
method Solve variational inequality to find value functions and optimal thresholds.
result Existence and expressions of optimal stopping times under specific conditions.
Study optimal stopping times for financial options with negative discount rates and random refraction times.
problem Optimal stopping times for financial options with negative discount rates and random refraction times.
method Analyzes optimal multiple stopping problems driven by Lévy processes with negative discount rates and random refraction times.
result Optimal strategy is uniquely characterized by up-crossing times, with thresholds determined explicitly or recursively.
New method models stopping times that can be equal with non-zero probability.
problem Standard stopping time models assume conditional independence, limiting flexibility.
method Modified Cox construction with bivariate exponential distribution.
result Created a family of stopping times that can be equal with positive probability.
Study optimal stopping and a non-zero-sum game with risk measures in discrete time.
problem Optimal stopping and risk assessment in discrete time with non-zero-sum game.
method Using g-expectations and recursive procedures, construct Nash equilibrium. result Construct Nash equilibrium for a non-zero-sum game with risk measures.
Two stopping criteria proposed for real-time fMRI experiments.
problem Developing accurate stopping criteria for real-time fMRI experiments.
method Empirical study of two proposed stopping criteria.
result Performance of two stopping criteria empirically studied.
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time…
Paper solves non-Markovian optimal stopping problems using discrete approximations.
problem Non-Markovian optimal stopping problems in continuous-time processes.
method Discrete-type approximation scheme based on variational inequalities.
result Constructs ε-optimal stopping times and optimal values in full generality.
Optimizes timing for buying and selling assets with a trailing stop.
problem Timing optimal buy and sell points for assets with a trailing stop.
method General linear diffusion framework, optimal double stopping problem, numerical method.
result Proves the optimality of using a sell limit order in conjunction with the trailing stop.
This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…
Early stopping improves sample quality in latent diffusion models.
problem Latent diffusion models degrade sample quality with conventional early stopping.
method Analyzed the interaction between latent dimension and stopping time under Gaussian framework.
result Lower-dimensional representations benefit from earlier termination, higher-dimensional spaces require later stopping.
The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.
problem Investigating the properties of semi-symmetric metric connections in perfect fluid space-time.
method Using concircularly semi-symmetric metric connections, the study derives conditions for quasi-Einstein manifolds and examines the scalar curvature of perfect fluid space-times.
result The study proves that in a perfect fluid space-time, the scalar curvature is constant and represents a phantom barrier.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…
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…
A framework for robust exploration in reinforcement learning under ambiguity.
problem Optimal stopping under ambiguity in reinforcement learning.
method Continuous-time robust reinforcement learning framework using g-expectation and backward stochastic differential equations. result Constructs a robust exploratory stopping time approximating the optimal stopping time under ambiguity.
Study naive vs sophisticated agents stopping a diffusion process with time-inconsistent payoffs.
problem Time-inconsistent stopping problem for diffusion processes.
method Analyzes naive and sophisticated agents' strategies, proving equilibrium existence.
result Equilibrium strategies can be derived as fixed points of strategic reasoning operators.
New algorithms use Gaussian processes to optimize stopping times in financial markets.
problem Optimizing stopping times in financial time series with specific applications.
method Gaussian and Deep Gaussian Process models to analytically evaluate optimal stopping value functions and policies.
result Proposed algorithms outperform benchmarks on various financial time series datasets.
Probabilistic proof of smooth boundaries in optimal stopping problems.
problem Continuous differentiability of time-dependent optimal boundaries in optimal stopping problems.
method Local probabilistic arguments for a wider range of conditions.
result First probabilistic proof of continuous differentiability under general conditions.
This work bounds the run-time of nonconvex optimization with early stopping.
problem Bounding the expected run-time of nonconvex optimization with early stopping.
method Derives conditions for well-defined early stopping based on validation function norms and bounds the expected number of iterations and gradient evaluations.
result Guarantees the validity of early stopping and provides bounds on the expected run-time for various optimization algorithms.
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller's) and long (buyer's) positions in an Americ…