Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
Study proves optimal controls for stochastic Volterra equations with singular kernels.
problem Existence of optimal controls for stochastic Volterra equations with singular kernels.
method Sufficient conditions based on integrability and growth hypotheses.
result Existence of optimal relaxed and strict controls under classical convexity assumptions.
Optimizes control of infectious disease spread using stochastic methods.
problem Optimizing control of highly infectious diseases like COVID-19.
method Reformulated Hamilton-Jacobi-Bellman equation as stochastic minimum principle, leading to forward-backward stochastic differential equations.
result Numerous numerical solutions presented under various scenarios.
A new method for stochastic optimal control improves accuracy over existing techniques.
problem Improving the accuracy of stochastic optimal control for noisy systems.
method Stochastic Optimal Control Matching (SOCM) using Iterative Diffusion Optimization (IDO) with path-wise reparameterization trick.
result SOCM achieves lower error than existing techniques for three out of four control problems, sometimes by an order of magnitude.
Paper generalizes LSMC algorithm for stochastic control problems.
problem Optimal decision problems with uncertainty.
method Backward simulation method with three pillars.
result Generalization of LSMC algorithm for a wide class of models.
Solves optimal dividend/consumption problem using stochastic control theory.
problem Optimal dividend and consumption decisions under controlled state process.
method Fixed point argument based on stochastic representation of linear equations.
result Smooth solution to Hamilton Jacobi Bellman equations.
Develops a new approach to optimal control of stochastic systems.
problem Optimal control of stochastic nonlinear dynamical systems is challenging.
method Formulates optimal control as input estimation, using probabilistic inference and Expectation Maximization.
result Extracts time-varying linear Gaussian feedback controllers from the joint state-action distribution.
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Solves optimal control with constraints for stochastic systems.
problem Optimal control of constrained stochastic linear-quadratic systems.
method State separation theorem and Riccati equations for explicit solution.
result Explicit piecewise affine optimal control policy.
Optimal strategies in stochastic control problems with two parameters are identified.
problem Optimal control strategies in stochastic processes with two parameters.
method First, parameters are chosen by continuous/smooth fit conditions. Then, optimality is shown using verification arguments.
result Optimal strategies can be concisely expressed via scale functions.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
A new ML algorithm solves complex economic control problems.
problem Solving high-dimensional, finite-horizon stochastic control problems in economics.
method Deep neural network representation of optimal policy functions with three key features.
result Efficiently solves various economic control problems including recursive utility and growth models.
Unified framework connects reinforcement learning and optimal control.
problem Sequential decision-making across different communities.
method Unified modeling framework based on optimizing policies.
result Unified framework includes four universal policy classes.
The paper solves a complex control problem with stochastic elements and switching conditions.
problem Non-homogeneous stochastic LQ control with regime switching and random coefficients.
method Explicit optimal control and value obtained through two systems of backward stochastic differential equations (BSDEs). Existence and uniqueness of solutions proved using BMO martingales and contraction mapping method.
result Explicit optimal state feedback control and optimal value derived for the problem.
Optimizes dividend policies in a Brownian model with controlled rates.
problem Realistic optimal dividend policies in a stochastic control problem.
method Delayed linear control strategies for refracted diffusion processes.
result Optimality of delayed linear control strategies for dividend payments.
The Noether theorem is extended to stochastic control problems using contact symmetries.
problem Stochastic optimal control problems.
method Exploiting jet bundles and contact geometry, the authors prove the existence of conserved quantities.
result Optimal control problems admit infinitely many conserved quantities in the form of local martingales.
Study optimizes investment decisions with fixed costs using stochastic control methods.
problem Optimizing irreversible investment decisions with fixed adjustment costs.
method Stochastic impulse control approach, viscosity solutions, quasi-variational inequality.
result Characterization of optimal control and sensitivity analysis in linear case.
Solves optimal control for stochastic processes with absorbing states.
problem Optimal control of stochastic processes with absorbing states.
method Solves through system of partial differential equations.
result Explicit solution for Merton portfolio problem with default probability.
New method optimizes pumped hydroelectric storage with state constraints.
problem Optimal management of pumped hydroelectric production with state constraints.
method Transformed constrained problem into an unconstrained one in augmented spaces with state constraints penalized.
result Solved the problem using dynamic programming.
FinFlowRL learns from experts to optimize financial control in changing markets.
problem Traditional finance control methods fail in real-world, non-stationary markets.
method Imitation-Reinforcement Learning framework that pretrains on expert strategies and finetunes in noise space.
result Consistently outperforms individually optimized experts across diverse market conditions.
This paper develops scalable control variates for Monte Carlo methods using stochastic optimization.
problem Reducing variance in Monte Carlo estimators for large-scale problems.
method Control variates based on Stein operators, optimized through stochastic optimization.
result Novel theoretical results and empirical validations show effective variance reduction.
The paper solves optimal control problems for stochastic delay equations.
problem Optimal control of stochastic delay differential equations.
method Rewriting the problem in an infinite-dimensional Hilbert space, using dynamic programming and viscosity solutions.
result Characterizes the value function as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.
Study optimal trading strategies for futures contracts using stochastic control.
problem Optimizing dynamic trading of futures contracts over a finite horizon.
method Formulate a utility maximization problem based on the Schwartz 97 model, solve HJB equation to derive optimal strategies.
result Derive optimal dynamic trading strategies in closed form for single or multiple futures contracts.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
Deep learning approximates high-dimensional stochastic control problems.
problem High-dimensional stochastic control problems with the curse of dimensionality.
method Approximates time-dependent controls as neural networks and trains them through model dynamics.
result Achieves satisfactory accuracy in high-dimensional problems.
Optimizes control of noisy discrete systems without system matrix knowledge.
problem Optimal control of discrete-time systems with additive and multiplicative noises.
method Stochastic Lyapunov and Riccati equations, model-free reinforcement learning.
result Model-free reinforcement learning algorithm converges to optimal control policy.
The paper studies complex equations for financial optimal control problems.
problem Optimal control problems with unspecified dynamics in financial modeling.
method First Order BSPDEs in higher dimensions.
result Constructs value functions for optimal control problems.
Paper develops a novel approach for optimal control using kernel methods.
problem Optimal control of nonlinear stochastic systems.
method Infinitesimal generator approach in reproducing kernel Hilbert spaces.
result Data-driven solution to optimal control problems.
NOVAS uses adaptive stochastic search for non-convex optimization in deep networks.
problem Non-convex optimization challenges in deep neural networks.
method Adaptive stochastic search for non-convex optimization.
result NOVAS outperforms existing alternatives in a structured prediction task.
Unified framework connects stochastic optimization to Bayesian inference.
problem Stochastic optimization algorithms and their theoretical underpinnings.
method Latent variational problem and Forward Backward Stochastic Differential Equations (FBSDE).
result Recovery of various adaptive stochastic gradient descent methods.
New algorithm achieves optimal regret in non-stochastic control, showing stochasticity is not beneficial.
problem Achieving optimal control in non-stochastic systems with adversarial noise.
method Novel online Newton step algorithm adapted to adversarial disturbances, using policy regret bounds.
result Optimal O ~ ( T ) \widetilde{\mathcal{O}}(\sqrt{T}) O ( T ) regret achieved in unknown dynamics, p o l y ( log T ) \mathrm{poly}(\log T) poly ( log T ) regret in known dynamics. Researchers use Meyer-σ-fields to model information flow in irreversible investment problems.
problem Modeling information flows in stochastic control problems with jumps.
method Using Meyer-σ-fields as a tool to model information flow.
result Different signals on exogenous jumps lead to different optimal controls.
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
The paper proposes a new method to estimate optimal policies using MCMC.
problem Estimating the optimal policy for systems with unknown dynamics and reward functions.
method Using Markov Chain Monte Carlo to generate samples from the posterior distribution of parameters conditioned on optimality.
result The method provably converges to the globally optimal stochastic policy with similar variance to policy gradient methods.
Optimizes trading in markets with unpredictable price impacts.
problem Optimizing trading strategies in markets with stochastic price impacts.
method Singular perturbation methods to approximate optimal control problem.
result Proves approximations are accurate to specified order using sub- and super-solutions.
Deep neural networks solve stochastic control problems with delay.
problem Challenges in stochastic control problems with delay due to path-dependence and high dimensions.
method Employing recurrent neural networks (RNNs) to parameterize policies and optimize objectives.
result RNNs, especially LSTMs, efficiently capture path-dependence and outperform feedforward networks in training and performance.
We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise a novel class of iterative solutions to the stochastic optimal control problem …
A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
New control strategy minimizes infected individuals in SIS epidemics.
problem Developing effective control strategies for SIS epidemics.
method Stochastic optimal control of SDEs with jumps, using treatment intensities.
result Control strategy consistently outperforms alternatives in synthetic data.
Solves optimal control for a specific type of stochastic equation.
problem Optimal control of a conditional McKean-Vlasov equation with random coefficients.
method Dynamic programming approach and backward stochastic Riccati equations.
result Characterizes time-consistent optimal control strategies.
Study optimal pairs trading with transaction costs using stochastic control.
problem Finding optimal trade times and shares in pairs trading with proportional costs.
method Singular stochastic control approach to solve a nonlinear quasi-variational inequality.
result Developed a discrete time dynamic programming algorithm to compute transaction regions.
New control theory for self-path-dependent problems solves unique constraints.
problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.
The paper tackles robust control with uncertain dependence using data-driven methods.
problem Nonparametric robust control under dependence uncertainty in multi-period stochastic systems.
method Nonparametric adaptive robust control framework using stochastic gradient descent ascent algorithm.
result The controller benefits from knowing more about the uncertain model.
Optimizes CM for stochastic convex optimization with progressive precision.
problem Stochastic nature of objective function in convex optimization.
method Iterative coordinate minimization with optimal precision control.
result Order-optimal regret performance for strongly convex and nonsmooth functions.
This work formalizes guidance in diffusion models and introduces a stochastic control framework.
problem Lack of a solid theoretical foundation for guidance scheduling in diffusion models.
method Introduces a stochastic optimal control framework to cast guidance scheduling as an adaptive optimization problem.
result Establishes a principled foundation for more effective guidance in diffusion models.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
A new approach optimizes weights in DLP for better risk-adjusted performance.
problem Optimizing time-varying weights in Double Linear Policy (DLP) for better risk-adjusted performance.
method Stochastic Model Predictive Control (SMPC) framework to maximize risk-adjusted returns while enforcing constraints.
result Empirical results show improved risk-adjusted performance and drawdown control.
Agent learns optimal control inputs for plants with unknown parameters.
problem Optimal control for systems with unknown and changing parameters.
method Personalized control inputs based on stochastic dynamics.
result Demonstrated effectiveness on simulated system.