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.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
The paper solves recursive optimal stopping problems in stock trading.
problem Optimal stopping in recursive optimal stopping problems with applications to stock trading.
method Introduced a class of recursive optimal stopping problems and showed well-posedness in a Markovian setting. Determined optimal stopping rules in stock trading models.
result The value function is the unique solution to a fixed point problem and an optimal stopping time exists.
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.
Solves optimal stopping problem for financial technical analysis.
problem Optimal stopping problem for technical analysis models.
method Wide-class dynamics modeling support/resistance lines.
result Solution to optimal stopping problem for technical analysis.
Dual martingales improve primal optimal stopping problem efficiency.
problem Optimal stopping problem in the primal formulation.
method Investigation of dual martingales to improve primal methods.
result Accurate dual martingale approximations reduce primal problem variance.
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.
problem Optimal stopping problem in continuous time with random exploration.
method Transformed optimal stopping to optimal control problem, derived HJB equation, designed reinforcement learning algorithm.
result Convergence rate of policy iteration and comparison to classical optimal stopping.
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
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
MUSE provides unbiased stopping estimates for optimal problems.
problem Estimating the utility of optimal stopping problems.
method Backward recursive construction of the Multilevel Unbiased Stopping Estimator (MUSE).
result MUSE achieves ε-accuracy with O(1/ε^2) computational cost.
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.
problem Optimal stopping problems in randomized algorithms.
method Forward and backward Monte Carlo based optimisation algorithms.
result Proved convergence of the proposed algorithms and derived convergence rates.
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…
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.
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.
Deep neural networks can solve optimal stopping problems without dimensionality issues.
problem Optimal stopping problems in high-dimensional state spaces.
method Established a general framework for deep ReLU neural networks to approximate value functions and continuation values.
result Deep neural networks can approximate value functions and continuation values with error at most ε of size κd^q ε^(-r).
New method solves optimal stopping problems using rough path signatures.
problem Optimal stopping problems in finance and other fields.
method Using rough path signatures and deep neural networks.
result Solves optimal stopping problems efficiently under minimal assumptions.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
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.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
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.
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.
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.
A new method uses deep learning for optimal stopping problems.
problem Solving optimal stopping problems in financial mathematics.
method Deep primal-dual BSDE framework with a novel loss function.
result The method provides a true upper bound for the optimal value.
New method uses reinforced regression for solving optimal stopping problems.
problem Solving optimal stopping problems in mathematical finance.
method Reinforced regression based on previously estimated continuation values.
result Illustrated by a numerical example from mathematical finance.
New algorithm for non-Markovian optimal stopping problems using Brownian motion.
problem Optimal stopping time problems for non-Markovian state processes.
method Longstaff-Schwartz-type algorithm based on statistical learning theory.
result Error estimates for approximation architecture spaces with finite Vapnik-Chervonenkis dimension.
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.
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities 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…
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.
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…
Direct method solves complex option pricing in changing market conditions.
problem Pricing financial options with changing market conditions.
method Reduces complex optimal stopping problems to simpler ones, finding explicit value functions.
result Simpler and more direct solution for option pricing in regime-switching models.
Paper approximates free boundary for optimal investment stopping problems.
problem Optimal investment stopping problems with utility maximization.
method Dual control method to derive asymptotic properties and construct a global closed-form approximation.
result Global closed-form approximation of dual free boundary reduces computational cost.
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.
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…
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.
Improved algorithm for optimal stopping problems reduces runtime.
problem Optimal stopping problems with infinite time horizon and random discounting.
method Flexible forward improvement iteration with a variable look-ahead distance.
result The new algorithm converges and can significantly reduce runtime.
A new method solves complex financial problems using deep learning.
problem Optimal stopping and option pricing in finance.
method Compound BSDE method, based on reformulating BSDEs.
result The method offers accurate and efficient solutions for high-dimensional problems.
A new algorithm approximates optimal stopping problems with semi-tractable complexity.
problem Approximating the value of optimal stopping problems in discrete and continuous time.
method Weighted Stochastic Mesh (WSM) Algorithm for discrete and continuous time optimal stopping problems.
result WSM leads to semi-tractable complexity in discrete cases, with complexity bounded by ε−4logd+2(1/ε). Optimizes selling bonds with non-negative prices using a Brownian bridge model.
problem Maximizing the expected value of an exponential gain function on a Brownian bridge.
method Develops pathwise properties of the Brownian bridge and uses martingale methods of optimal stopping theory.
result Solves the stopping problem for the exponential of a Brownian bridge.
Improved reinforcement learning with emergency stops.
problem Reducing exploration in reinforcement learning.
method Emergency stop mechanisms to reduce sample complexity.
result Significant improvement in sample complexity and speed.
The paper tackles ICU discharge strategies by evaluating optimal stopping scenarios.
problem Optimal stopping in ICU discharge with complex causal inference challenges.
method Generalized g-formula implementation and application to MIMIC-IV dataset.
result Improved ICU discharge strategies demonstrated with the g-formula approach.
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.
Study optimal timing to divest from assets with uncertain future scenarios.
problem Optimal timing to divest from assets with uncertain future scenarios.
method Smooth model of decision making under ambiguity aversion, optimal stopping problem with learning.
result Proves a minimax result reducing the problem to standard optimal stopping problems with learning.