Tootfinder

This https://arxiv.org/abs/2312.03941 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimising Numbers of Losses and Abandonments in Small Call Centres Under a Transient Regime
We consider the problem of allocating customers to agents in small call centres so that transient performance indicators in terms of expected numbers of losses and abandonments are optimised. To gain insight into the general structure of optimal policies, we start by (i) using backward induction based upon Bellman's equation for a finite-horizon discrete-time model, and (ii) deriving stationary policies for an infinite-horizon continuous-time model with discounting. We then compare the performa…

Stochastic Optimal Control with Control-Dependent Diffusion and State Constraints: A Degenerate Elliptic Approach
Anderson O. Calixto, Bernardo Freitas Paulo da Costa, Glauco Valle
https://arxiv.org/abs/2508.04809

Stochastic Optimal Control with Control-Dependent Diffusion and State Constraints: A Degenerate Elliptic Approach
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear, degenerate elliptic Hamilton--Jacobi--Bellman (HJB) equation with a nontrivial Neumann boundary condition. Although these features have been studied separately, this work provides the first unified treatment combining them all. We establish that the optimal value f…

Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Martin Hutzenthaler, Tuan Anh Nguyen
https://arxiv.org/abs/2506.23969

Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Full history recursive multilevel Picard (MLP) approximations have been proved to overcome the curse of dimensionality in the numerical approximation of semilinear heat equations with nonlinearities which are globally Lipschitz continuous with respect to the maximum-norm. Nonlinearities in Hamilton-Jacobi-Bellman equations in stochastic control theory, however, are often (locally) Lipschitz continuous with respect to the standard Euclidean norm. In this paper we prove the surprising fact that M…

This https://arxiv.org/abs/2411.15174 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Regularity for Weak Solutions to First-Order Local Mean Field Games
We establish interior regularity results for first-order, stationary, local mean-field game (MFG) systems. Specifically, we study solutions of the coupled system consisting of a Hamilton-Jacobi-Bellman equation $H(x, Du, m) = 0$ and a transport equation $-\operatorname{div}(m D_pH(x, Du, m)) = 0$ in a domain $Ω\subset \mathbb{R}^d$. Under suitable structural assumptions on the Hamiltonian $H$, without requiring monotonicity of the system, convexity of the Hamiltonian, separability in variables…

Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning
Yuhua Zhu, Yuming Zhang, Haoyu Zhang
https://arxiv.org/abs/2506.05208

Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning
This paper addresses continuous-time reinforcement learning (CTRL) where the system dynamics are governed by a stochastic differential equation but are unknown, and only discrete-time observations are available. Existing approaches face limitations: model-based PDE methods suffer from non-identifiability, while model-free methods based on the optimal Bellman equation (Optimal-BE) are prone to large discretization errors sensitive to both the dynamics and reward structure. To overcome these chal…

This https://arxiv.org/abs/2405.16643 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

The Hamilton-Jacobi-Bellman Equation in Economic Dynamics with a Non-Smooth Fiscal Policy
We consider a class of economic growth models that includes the classical Ramsey--Cass--Koopmans capital accumulation model and verify that, under several assumptions, the value function of the model is the unique viscosity solution to the Hamilton--Jacobi--Bellman equation. Moreover, we discuss a solution method for these models using differential inclusion, where the subdifferential of the value function plays an important role. Next, we present an assumption under which the value function is…

Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error
Armin Gie{\ss}ler, Albertus Johannes Malan, S\"oren Hohmann
https://arxiv.org/abs/2506.09685

Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error
In this paper, we present a novel method for computing the optimal feedback gain of the infinite-horizon Linear Quadratic Regulator (LQR) problem via an ordinary differential equation. We introduce a novel continuous-time Bellman error, derived from the Hamilton-Jacobi-Bellman (HJB) equation, which quantifies the suboptimality of stabilizing policies and is parametrized in terms of the feedback gain. We analyze its properties, including its effective domain, smoothness, coerciveness and show th…

On Exact Solutions to the Linear Bellman Equation
David Ohlin, Richard Pates, Murat Arcak
https://arxiv.org/abs/2506.15527 https://ar…

On Exact Solutions to the Linear Bellman Equation
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semili…

Winners vs. Losers: Momentum-based Strategies with Intertemporal Choice for ESG Portfolios
Ayush Jha, Abootaleb Shirvani, Ali Jaffri, Svetlozar T. Rachev, Frank J. Fabozzi
https://arxiv.org/abs/2505.24250

Winners vs. Losers: Momentum-based Strategies with Intertemporal Choice for ESG Portfolios
This paper introduces a state-dependent momentum framework that integrates ESG regime switching with tail-risk-aware reward-risk metrics. Using a dynamic programming approach and solving a finite-horizon Bellman equation, we construct long-short momentum portfolios that adjust to changing ESG sentiment regimes. Unlike traditional momentum strategies based on historical returns, our approach incorporates the Stable Tail Adjusted Return ratio and Rachev ratio to better capture downside risk in tu…

Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
Dingqian Gao, Qi L\"u
https://arxiv.org/abs/2507.01407 https://

Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function. We then prove the existence, uniqueness of viscosity solutions to the HJB equation, along with their continuous dependence on initial data and model parameters. Finally, under appropriate regularity conditions on the value function…

Mean Field Games without Rational Expectations
Benjamin Moll, Lenya Ryzhik
https://arxiv.org/abs/2506.11838 https://arxiv.org/pdf/250…

Mean Field Games without Rational Expectations
Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common noise, this assumption results in the "Master equation" (a.k.a. "Monster equation"), a Hamilton-Jacobi-Bellman equation in which the infinite-dimensional density of agents is a state variable. The rational expectations assumption and the implication that agents so…

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor
Xun Tang, Nan Sheng, Lexing Ying

This https://arxiv.org/abs/2411.13111 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal investment problem in a renewal risk model with generalized Erlang distributed interarrival times
This paper explores the optimal investment problem of a renewal risk model with generalized Erlang distributed interarrival times. The phases of the Erlang interarrival time is assumed to be observable. The price of the risky asset is driven by the constant elasticity of variance model (CEV) and the insurer aims to maximize the exponential utility of the terminal wealth by asset allocation. By solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we establish the concavity of the va…

A primer of optimal ergodic average control for an insurance company diffusion model
Elizaveta Iashchenko, Alexander Veretennikov
https://arxiv.org/abs/2506.19134

A primer of optimal ergodic average control for an insurance company diffusion model
An ergodic analogue of a well-known diffusion model for risk and dividend distribution of a financial company is considered. In this simple primer it is curious how infinitely many optimal strategies are in accordance with the ergodic Bellman equation.

Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control
Peter Bank, Franziska Bielert
https://arxiv.org/abs/2507.08657 https:/…

Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential equation. We combine the martingale optimality principle with a functional form of Itô's formula to derive a Hamilton-Jacobi-Bellman (HJB) equation for this problem. This HJB equation is formulated in terms of Dupire's functional derivatives and involves a transpor…

Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertainty
Ziyu Li, Chen Fei, Weiyin Fei
https://arxiv.org/abs/2506.13207

Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertainty
Considering that the decision-making environment faced by reinforcement learning (RL) agents is full of Knightian uncertainty, this paper describes the exploratory state dynamics equation in Knightian uncertainty to study the entropy-regularized relaxed stochastic control problem in a Knightian uncertainty environment. By employing stochastic analysis theory and the dynamic programming principle under nonlinear expectation, we derive the Hamilton-Jacobi-Bellman (HJB) equation and solve for the …