New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
New tools for uncertainty in dynamical systems without distribution assumptions.
problem Uncertainty representation in dynamical systems without distributional assumptions.
method Kernel mean embedding and kernel probabilistic programming.
result Distribution-free representation, comparison, and propagation of uncertainties.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
The paper develops deep learning algorithms for solving complex stochastic control problems.
problem High-dimensional stochastic control problems
method Approximate optimal policy with neural networks, value function with Monte Carlo regression, using performance or hybrid iteration.
result The algorithms provide a theoretical justification and analyze consistency and rate of convergence for control and value function estimates.
The paper analyzes error propagation in dynamic programming for stochastic control and option pricing.
problem Error propagation in dynamic programming for stochastic control and option pricing.
method Formulated a general dynamic programming framework, used RKHSs for nonparametric regression, and Monte Carlo subsampling for estimating continuation value.
result Proposed a rigorous error decomposition and control mechanism for error propagation in dynamic programming.
Deep learning solves complex stochastic control with jumps.
problem Solving high-dimensional stochastic control tasks with jumps.
method Model-based approach using two neural networks, iteratively trained with objectives derived from the Hamilton-Jacobi-Bellman equation.
result Demonstrates effectiveness in solving complex high-dimensional stochastic control tasks.
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
The paper develops algorithms for computing in stochastic acceptors.
problem Computing input marginals and acceptance probabilities in stochastic acceptors.
method Dynamic programming for input marginals, EM for parameter estimation.
result Efficient algorithms for computing in stochastic acceptors.
Neural model accelerates SDDP for stochastic optimization.
problem Exponential complexity of SDDP limits its applicability to low-dimensional problems.
method Trainable neural model maps problem instances to a low-dimensional piecewise linear value function.
result ν-SDDP significantly reduces problem solving cost without sacrificing solution quality.
New metric derived for robust optimization in stochastic control problems.
problem Non-parametric uncertainty in multiperiod stochastic control problems.
method Derived a new metric, adapted (p,∞)--Wasserstein distance, and used dynamic programming principle. result Dynamic programming principle for DRO problems with semi-separable cost functions.
The paper evaluates dynamic hedging strategies for various financial products.
problem Pricing derivative products with dynamic hedging and issuer-tailored risk.
method Unified constrained discrete stochastic dynamic programming framework with sequential local minimizing strategies.
result Demonstrates flexibility of the unified framework through numerical examples.
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
New method uses dynamic programming for meta continual learning.
problem Challenges of generalization and catastrophic forgetting in sequential learning.
method Developed a theoretical framework using dynamic programming for meta continual learning.
result Theoretical and practical method achieves better accuracy than existing methods.
We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of …
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…
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…
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.
Paper explores two methods for optimal portfolio selection in financial markets.
problem Optimal portfolio selection for financial markets with jumps.
method Maximum principle and dynamic programming approach.
result Relationship between two methods and their adjoint processes.
In this paper, we consider the problem of optimization of a portfolio consisting of securities. An investor with an initial capital, is interested in constructing a portfolio of securities. If the prices of securities change, the investor shall decide on reallocation of the portfolio. At each moment of time, the prices…
Dynamic programming helps manage fisheries affected by random disturbances.
problem Managing fisheries affected by random disturbances.
method Dynamic programming approach to analyze and optimize management strategies.
result Dynamic programming is crucial for fully characterizing optimal harvest strategies.
The paper shows how label noise in training can lead to solutions that solve a Lasso program.
problem Understanding the implicit bias of training algorithms in overparametrised models.
method Analyzing the continuous time version of the training dynamics of a quadratically parametrised model.
result The stochastic flow implicitly solves a Lasso program, providing convergence guarantees and support recovery conditions.
Solves VaR-constrained portfolio optimization in markets with stochastic volatility.
problem Optimizing portfolio in markets with stochastic volatility under VaR constraints.
method Dynamic programming approach to Heston's stochastic volatility model.
result Optimal investment strategy linked to unconstrained problem via a vega-neutral derivative.
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Improved machine learning for reservoir optimization problems.
problem Optimizing control in high-dimensional storage problems.
method Modified dynamic programming algorithm with neural networks for Bellman values and conditional cuts.
result Neural networks outperform classical feedforward networks in estimating Bellman values.
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the …
Neural networks enhance linear programming for complex decision-making problems.
problem High-dimensional and combinatorial operations research problems.
method Hybrid solution method combining linear programming and neural networks.
result Neural network value function approximations outperform polynomial approximations in a transportation problem.
Study optimal investment and consumption in financial markets using Ornstein-Uhlenbeck process.
problem Optimal consumption/investment problem in financial markets with logarithmic utility.
method Stochastic dynamical programming method and Hamilton-Jacobi-Bellman (HJB) equation.
result Explicit solution to the HJB equation and optimal financial strategies constructed.
We study the performance of stochastically trained deep neural networks (DNNs) whose synaptic weights are implemented using emerging memristive devices that exhibit limited dynamic range, resolution, and variability in their programming characteristics. We show that a key device parameter to optimize the learning effic…
Model for optimal cybersecurity investment considering clustered cyberattacks.
problem Optimal investment in cybersecurity to reduce system vulnerability under clustered cyberattacks.
method Developed a continuous-time stochastic model using a Hawkes process, extended Gordon-Loeb model, solved as a Markovian stochastic optimal control problem.
result Investment policies that account for attack clustering lead to more effective and responsive strategies, improving upon static and Poisson-based approaches.
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 stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic/flexible pricing; and it is in thi…
Solves Merton's investment-consumption problem with certainty equivalent approach.
problem Maximizing CRRA utility of consumption over time and investment mix.
method Identifies a certainty equivalent problem for the Merton problem, reformulates it as an SOCP, and applies it to model predictive control.
result The certainty equivalent problem can be solved as an SOCP, facilitating model predictive control.
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.
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.
Stochastic programs simplify complex models with noise and nondeterminism.
problem Handling models with nuisance parameters, noise, and nondeterminism.
method Developed a reference implementation for stochastic probabilistic programs and inference.
result Efficient inference in models with noise and nondeterminism is possible.
Develops a model for bid and ask prices using stochastic control.
problem Modeling bid and ask prices of a European asset.
method Formulates a stochastic control problem, uses Girsanov theorem, Esscher transform, and dynamic programming.
result Derives equations to determine bid and ask prices.
Efficiently selects top-m designs for various contexts using sequential sampling.
problem Optimizing selection of top-m designs across different contexts.
method Formulated as a stochastic dynamic programming problem, developed sequential sampling policy.
result Asymptotically optimal sampling ratios for efficient selection.
New approach optimizes dynamic decisions with side info.
problem Optimizing decisions under uncertainty with additional data.
method Combines machine learning with robust optimization.
result Proves asymptotic optimality and achieves significant improvements.
The paper solves complex control problems using neural networks.
problem Solving McKean-Vlasov control problems.
method Mean-field neural networks and algorithms based on dynamic programming and stochastic maximum principle.
result Extensive numerical results show the accuracy of the proposed algorithms.
Improved reinforcement method for optimal control problems.
problem Optimal control problems with limited computational cost.
method Reinforced least squares Monte Carlo method for stochastic control problems.
result Significant improvement in method's efficiency and accuracy.
The paper solves multi-period portfolio selection with constraints using a dynamic factor model.
problem Multi-period mean-variance portfolio selection with constraints.
method Dynamic factor model, dynamic programming, piecewise linear feedback policy.
result Optimal portfolio policies determined by two stochastic processes.
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.
problem Optimal policies in finite-time MDPs are not stationary and require epoch-specific training.
method Introduces dynamic policy gradient combining dynamic programming and policy gradient, analyzes convergence for softmax parametrisation.
result Dynamic policy gradient training exploits finite-time structure, leading to better convergence bounds.
Develops RL for dynamic risk assessment in stochastic optimization.
problem Time-consistent risk assessment in stochastic optimization problems.
method Model-free reinforcement learning with dynamic convex risk measures, time-consistent dynamic programming, policy gradient updates, actor-critic neural network optimization.
result Demonstrates optimal policies for statistical arbitrage, financial hedging, and robot control.
An insurer optimizes investment in a market with bank account and risky assets, considering nonlinear economic factors.
problem Optimizing investment strategy for an insurer in a market with bank account and risky assets.
method Adapting dynamic programming approach, deriving Hamilton--Jacobi--Bellman (HJB) equation, proving unique solvability, and solving coupled FBSDEs.
result Derives the optimal investment strategy for an insurer.
Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.
problem Modeling price and storage dynamics in natural gas markets with path-dependent volatility.
method Developed a novel stochastic path-dependent volatility model and used deep learning for swing option pricing.
result Proposed a deep learning method for numerical approximations of swing option pricing.
BCI provides calibrated prediction intervals for time series forecasts.
problem Calibration of prediction intervals for time series forecasts.
method BCI wraps around any time series forecasting models and optimizes interval lengths using dynamic programming.
result BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence.
We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dyn…