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.
New framework for Bayesian inference using neural Schrödinger-Föllmer flows.
problem Approximate Bayesian inference in large datasets.
method Stochastic control, Schrödinger bridges, SDE-based models.
result Advocates stochastic control as a finite time and low variance alternative to SGLD.
Optimal market making strategy for electronic markets with persistent order flows.
problem Market making on electronic markets with persistent order flows.
method Formulated as a stochastic control problem, characterized by viscosity solutions, and implemented numerically.
result Characterization of an optimal market making strategy.
Model analyzes OTC market making with reputation feedback.
problem Optimizing electronic OTC liquidity provision considering reputation.
method Developed a stochastic-control model with feedback loops.
result Policy alternates between reputation-building and franchise monetization phases.
Model analyzes how reputation feedback affects OTC market making.
problem Understanding and optimizing OTC market making strategies.
method Developed a stochastic-control model with feedback loops.
result Policy alternates between reputation building and franchise monetization.
RWS outperforms current methods in learning SCFMs.
problem Learning models with stochastic control flow is challenging.
method Revisited reweighted wake-sleep algorithm for SCFMs.
result RWS learns better models and inference networks with more particles.
Adjoint Matching improves flow and diffusion models with reward fine-tuning.
problem Improving generative models with reward fine-tuning.
method Casting reward fine-tuning as stochastic optimal control (SOC) and enforcing a specific noise schedule.
result Adjoint Matching outperforms existing SOC algorithms.
Itô maps provide a method for any-step SDE integration.
problem Stochastic dynamics
method Itô map formulation
result Empirical results on synthetic and image-generation benchmarks
The paper fits cash management models to data using stochastic and linear programming.
problem Cash flow probability distribution assumptions in cash management models are relaxed.
method Stochastic and linear programming to fit models to data.
result A small random sample of data is sufficient to fit bound-based models.
We convert deterministic flow models to stochastic samplers.
problem Deterministic flow models are sensitive to errors and cannot condition on intermediate states.
method Transform ODEs into SDEs with the same marginal distributions.
result Empirically outperforms deterministic samplers and controls generation diversity.
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution withi…
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional…
Modeling financial system dynamics with interbank flows and borrowing.
problem Recreating financial crises like liquidity traps.
method Explicit solution of stochastic optimal control problems, focusing on utility maximization and central bank control.
result Explicit distribution of defaults in the financial system.
EnCF improves data assimilation for implicit, non-smooth observations.
problem Data assimilation challenges with implicit, many-to-one observations.
method EnCF uses a stochastic controlled flow to update forecast distributions.
result EnCF outperforms Kalman filters for non-Gaussian, implicit observations.
The paper solves a control problem using reflections to track a benchmark process.
problem Optimal consumption with a benchmark process that grows over time.
method Introduced two auxiliary state processes with reflections to transform the problem into a more tractable form.
result Established the existence of a unique classical solution to the dual PDE.
Model analyzes RFQ markets using stochastic control to optimize dealer performance and inventory.
problem Optimizing market making in aggregator-routed RFQ markets with varying dealer performance scores.
method Two-tier stochastic control model that separates RFQ-level price competition from macro routing.
result Optimal controls can be expressed through derivatives of reduced Hamiltonians, leading to interpretable mappings from optimal win probabilities to optimal offsets.
Unified reinforcement learning and stochastic processes with action-driven processes.
problem Combining reinforcement learning and stochastic processes for efficient control.
method Action-driven processes, leveraging control-as-inference, and minimizing Kullback-Leibler divergence.
result Action-driven processes unify reinforcement learning and stochastic processes, equivalent to maximum entropy reinforcement learning.
PLoM learns stochastic solutions to PDEs with limited data.
problem Synthesizing solutions to nonlinear PDEs with scarce data.
method Probabilistic Learning on Manifolds constrained by PDEs.
result Learned stochastic solutions minimize PDE residuals.
New formulation tackles arbitrage in volatile markets using eigenvalue bounds.
problem Arbitrage opportunities in volatile markets beyond a certain time horizon.
method Formulated as a stochastic optimal control problem, solved via PDE.
result Characterized arbitrage time horizon through PDE solution.
A simple strategy optimizes broker-client trading, reducing price discounts for informed traders.
problem Optimizing broker-client trading to balance client flow and informed trader losses.
method Modelled as a stochastic control problem, derived optimal strategy in closed form, introduced algorithm.
result Optimal strategy reduces price discounts for informed traders, balancing client flow and informed trader losses.
The paper analyzes reg-SGD for convex problems, proving convergence and quantifying the rate of convergence.
problem Minimizing convex, L-smooth functions in a Hilbert space.
method Regularized stochastic gradient descent with decaying regularization.
result Strong convergence to the minimum-norm solution without boundedness assumptions.
A new framework for generative modeling using value-driven transport.
problem Developing efficient methods for generative modeling.
method A discrete-time stochastic control formulation of measure transport, formulated as a linear program with dual variables corresponding to the optimal value function.
result Well-trained VDT policies lead to straight transport paths that can be simulated quickly and robustly.
Paper characterizes equilibrium strategies for stochastic control with higher-order moments.
problem Stochastic control problems with higher-order moments.
method Novel characterization of time-consistent control problems, deriving equilibrium conditions via BSDEs.
result Derives sufficient and necessary conditions for an open-loop Nash equilibrium control (ONEC) in a novel way.
Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.
problem Time inconsistency in stochastic differential games.
method Proves existence and uniqueness of solutions to nonlocal fully-nonlinear parabolic systems.
result Generalizes stochastic game theory to include time-inconsistent preferences.
Unified framework for training diffusion and flow models to sample from target distributions.
problem Training diffusion and flow models to sample from target distributions defined by exponential tilting.
method Unified framework combining stochastic optimal control and non-equilibrium thermodynamics perspectives.
result Unified bias-variance decompositions and theoretical support for adjoint-based methods.
Model optimizes trading strategy with unobservable toxicity.
problem Maximizing daily trading profit with unobservable toxicity.
method Formulated as a partially observable stochastic control problem, solved in two steps.
result P&L performance gap is negligible (0.01%) in all scenarios.
Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
problem Time-inconsistent stochastic control problems with mean and higher-order moments.
method Developed closed-loop and open-loop Nash equilibrium controls using PDEs and maximum principles.
result Identical closed-loop and open-loop Nash equilibria controls, independent of state value and random path.
A scalable algorithm for sampling and fine-tuning models using Tilt Matching.
problem Efficient sampling and fine-tuning of generative models.
method Tilt Matching, arising from a dynamical equation, minimizes variance and inherits regularity from stochastic interpolants.
result Empirically verified to be efficient and highly scalable, providing state-of-the-art results.
This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We …
Market maker optimizes quotes under hidden Markov chain uncertainty.
problem Optimizing quotes in a market with unknown hidden factors.
method Stochastic control, filtering, and dynamic programming.
result Optimal spreads are biased under partial information.
Optimal control problem for firm cash flow with dividend and capital injection strategies.
problem Maximizing dividends while managing capital injections in a firm's cash flow.
method Proved two optimal strategies: mean-reverting dividends with capital injections or no injections until ruin.
result Optimal strategies are dichotomous: either mean-reverting dividends with injections or no injections.
Game theory model for optimal trading with end-of-day constraints.
problem Optimal trading strategy in a game between slow and fast traders.
method Coupled stochastic control problems, Fredholm integral equation solution.
result Explicit solution to the game with profitable strategies for both players.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
This work classifies SOC loss functions based on their gradient properties.
problem Optimizing noisy systems in stochastic optimal control.
method Grouping loss functions into classes with the same gradient expectation.
result Different loss functions have the same optimization landscape but differ in gradient variance.
Paper proposes efficient image inversion and editing using rectified stochastic differential equations.
problem Inversion and editing of real images using generative models.
method Proposes RF inversion using dynamic optimal control and a linear quadratic regulator, extending to stochastic sampler for Flux.
result Allows state-of-the-art performance in zero-shot inversion and editing, outperforming prior works.
DNN policies improve stochastic AC OPF for power grid optimization.
problem Optimizing power grid operations under uncertainty.
method Deep neural network (DNN) policies for real-time generator dispatch decisions.
result DNN policies enforce feasibility constraints and produce near optimal solutions.
Develops a framework for analyzing neural networks and ODE models using control theory.
problem Analyzing deep neural networks and neural ODE models trained with stochastic gradient algorithms.
method Identifies connections between control theory, deep learning, and statistical sampling; derives Pontryagin's optimality principle and Mean-Field Langevin dynamics.
result Derives explicit convergence rates and provides quantitive bounds on generalization error, showing dimension-independent rates.
Optimal control of reserve assets for stablecoins to maintain peg stability.
problem Balancing immediate liquidity and yield on reserve assets for stablecoin peg maintenance.
method Developed a stochastic model predictive control framework with moment closure for event intensities, incorporating a soft-thresholding structure for rebalancing.
result Optimal policy shifts predictably toward cash as expected outflows intensify or windows lengthen, preserving most bill carry in calm markets and quickly building cash during stress.
Investors' strategic trading affects asset prices, modeled as a game.
problem Investors' trading rates influence asset prices in dynamic markets.
method Model as a non-zero sum singular stochastic differential game, establishing equivalence between best-response and auxiliary control problems.
result Unique Nash equilibrium is deterministic with a closed-form solution.
Unified theory of θ-expectations derived from chaotic dynamics.
problem Non-convex stochastic control problems outside G-expectations.
method Spectral theory of transfer operators for uniformly hyperbolic flows, viscosity solutions to HJB equations.
result Affine Hessian, non-convex gradient structure of θ-expectation. New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
problem Constructing Birkhoff sections for pseudo-Anosov flows with specific properties.
method Uses connection between pseudo-Anosov flows and veering triangulations to explicitly construct sections with controlled complexity.
result Shows that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.
Two proofs of Kalman Theorem using flows of vector fields.
problem Classical result of Control Theory (Kalman Theorem).
method Two proofs using flows of vector fields.
result New criteria for local controllability of non-linear systems.
MFMs enable efficient reward alignment for generative models.
problem Computational bottleneck in controlling generative models.
method Meta Flow Maps (MFMs) extend consistency models and flow maps to stochastic regime for efficient value function estimation.
result MFMs enable inference-time steering and unbiased, off-policy fine-tuning to general rewards efficiently.
DeepMPC uses neural networks to control complex fluid flows efficiently.
problem Controlling complex fluid flows in real-time is challenging due to high dimensionality and multi-scale dynamics.
method Deep learning, specifically recurrent neural networks (RNNs), embedded in model predictive control (MPC) framework.
result Significant improvements in control performance achieved through online updates to prediction accuracy.
Ricci flow controls curvature on manifolds with bounds.
problem Controlling curvature on manifolds with given bounds.
method Ricci flow with curvature bounds and entropy controls.
result Global curvature control at positive times for manifolds.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
Market makers optimize bid/ask quotes under hidden Markov chain uncertainty.
problem Optimizing market quotes with hidden factors affecting order intensities.
method Solves stochastic control problem using filtering, control, and PDMPs theory.
result Value function is unique viscosity solution of dynamic programming equation.