We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all linear-in-momenta Casimirs on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation o…
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48 results for “dual control problem”
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical technique for obtaining an estimate of the value function which improves on purely…
A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuationmath.OC
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we s…
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer (1999) for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the f…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we der…
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is contin…
Optimal insurance demand under marked point processes shocks: a dynamic programming duality approachmath.OC
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…
We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian path…
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.
Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future observations, offers a principled solution, but is intractable. We review, then…
In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows…
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 …
An Efficient Implementation of Edge-Based Discretization without Forming Dual Control Volumesmath.NA
A simpler edge-based discretization method without dual volumes.
problem Efficiently computing edge-based discretization vectors without forming dual volumes.
method Directly compute edge-midpoint vectors and reduce dual volume formation.
result Significant reduction in computing time for tetrahedral grids.
We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…
Two deep learning algorithms solve utility maximisation problems in finance.
problem Solving utility maximisation problems in finance with deep learning.
method Two algorithms: one for Markovian problems via HJB equation and 2BSDE, the other for non-Markovian problems via adjoint BSDE.
result Highly accurate results with low computational cost, solving problems with power, log, and non-HARA utilities in various models.
Machine-assisted treatment recommendations hold a promise to reduce physician time and decision errors. We formulate the task as a sequence-to-sequence prediction model that takes the entire time-ordered medical history as input, and predicts a sequence of future clinical procedures and medications. It is built on the …
The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk model. It is well known that the value function of this optimal control problem do…
A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximizationmath.OC
Paper tackles utility maximization with job-switching and retirement constraints.
problem Maximizing utility with job-switching and retirement constraints.
method Dual-martingale approach and double obstacle problem theory.
result Characterization of optimal job-switching strategy and wealth boundaries.
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as this is often practised in cont…
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.
Study optimal portfolio strategies with periodic evaluation under short-selling prohibition.
problem Optimal portfolio strategies with periodic evaluation under short-selling prohibition.
method Reformulate the original problem into an auxiliary one-period optimization problem and introduce dual control problem.
result Derive and verify the value function and optimal constrained portfolio for the original problem.
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context suitable for martingale optimal transportation or, more generally, for optimal tra…
Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of the optimization problem at hand. In the context of regression, this can be achiev…
Understanding the dual formulation for the hedging of path-dependent options with price impactmath.PR
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in …
Paper tackles offline CMDP problems with near-optimal algorithm and sample complexity bound.
problem Offline CMDP problems with only offline data available.
method DPDL algorithm using single-policy concentrability coefficient and deviation control mechanism.
result DPDL algorithm matches sample complexity lower bound with factor.
Investor optimizes stock investments with noisy future price signals.
problem Optimizing stock investments with uncertain future stock prices.
method Dynamic investment strategy with partial observation of Brownian motion.
result Closed-form solution for optimal investment problem.
Optimizes control of hybrid systems with multiple switching processes.
problem Optimal control of hybrid systems with multiple Markov switching processes.
method Combines two separate Markov chains into one synthetic chain, derives HJB equations, and solves the portfolio choice problem.
result Derives explicit solutions and value functions for the optimal control problem.
Trading strategy mimics optimal control with simple heuristic.
problem Maximizing profit in markets with limited optimal control.
method Using the gradient of the Bellman value function as effective microstructure alphas.
result Trading strategy approximates optimal behavior in long-term trades.
Constrained Quadratic Risk Minimization via Forward and Backward Stochastic Differential Equationsq-fin.PM
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimalit…
Extends portfolio optimization with two quasiconvex risk measures.
problem Optimizing portfolios with dual risk measures for multiple stakeholders.
method Dual problem formulation, bisection algorithm, duality results.
result Approximately optimal solutions can be achieved with prescribed optimality gap.
Graph neural networks optimize radio resource management policies for wireless networks.
problem Optimizing user selection and power control in wireless networks with fairness constraints.
method Formulated as a Lagrangian dual problem, RRM policies are parameterized by a GNN architecture trained on channel conditions.
result The method achieves superior tradeoff between average and 5th percentile rates, demonstrating fairness.
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…
Unified market making controls risk, arbitrage, and volatility surfaces.
problem Market making risk, arbitrage, and volatility surface consistency.
method Constrained RL and stochastic control for risk-sensitive execution and hedging.
result Agent achieves positive P&L with zero calendar and butterfly violations.
We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity pr…
Method solves nonconvex constrained optimization problems with a new augmented Lagrangian approach.
problem Nonconvex composite functional constraints with inequality constraints.
method First-order augmented Lagrangian method with smoothed prox-linear reformulation.
result Explicit convergence rates for the proposed method in terms of KKT residual.
Robust -learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a closed form solution of the HJB equation for power utility due to its homothetic pr…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to stu…
This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one…
Study optimal consumption and portfolio strategies with no-borrowing constraint in financial markets.
problem Maximizing utility from consumption under constraints in a stochastic environment.
method Lagrange duality and singular control problem to solve dynamic no-borrowing constraint.
result Retrieve optimal portfolio and consumption plans via dual singular control problem.
We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying…
This paper improves robot grasping by integrating meta-control and latent-space imagination.
problem Dual-system approaches fail to consider the reliability of the learned model when making multiple-step predictions.
method A meta-controller arbitrates between model-based and model-free decisions based on local reliability, encouraging actions that improve the model and generating imagined experiences for additional training.
result Our approach learns near-optimal grasping policies in dense- and sparse-reward environments, outperforming baseline and state-of-the-art methods.
The paper extends Merton's problem by adding benchmark tracking, finding optimal strategies.
problem Maximizing consumption utility with a trade-off against benchmark performance.
method Developed a convex duality theorem and derived optimal strategies for specific cases.
result Found optimal portfolio and consumption strategies for CRRA utility and geometric Brownian motion benchmarks.
Primal-dual regression approach for Markov decision processes with general state and action spacemath.NA
Develops a regression approach for solving MDPs with general state and action spaces.
problem Solving MDPs with large or infinite state and action spaces.
method Regression-based primal-dual martingale approach.
result Tight upper and lower approximations of value functions and optimal policies.
This paper examines how data affects risk measures in uncertain distributions.
problem How does distributional ambiguity affect risk measures?
method Formulated and derived simpler dual problems for infinite and finite dimensional robust moment problems.
result Developed theory and conducted experiments in inventory control and portfolio management.
Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networkscs.LG
In this paper, we propose a novel framework for approximating the explicit MPC law for linear parameter-varying systems using supervised learning. In contrast to most existing approaches, we not only learn the control policy, but also a "certificate policy", that allows us to estimate the sub-optimality of the learned …