Related papers: SIMPOL Model for Solving Continuous-Time Heterogen…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately,…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
For pricing American options, %after suitable discretization in space and time, a sequence of discrete linear complementarity problems (LCPs) or equivalently Hamilton-Jacobi-Bellman (HJB) equations need to be solved in a sequential…
We propose and analyze a randomization scheme for a general class of impulse control problems. The solution to this randomized problem is characterized as the fixed point of a compound operator which consists of a regularized nonlocal…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…
We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Homotopy Analysis Method (HAM) to decompose a nonlinear…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
Service platforms must determine rules for matching heterogeneous demand (customers) and supply (workers) that arrive randomly over time and may be lost if forced to wait too long for a match. Our objective is to maximize the cumulative…
When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…
We consider model-based multi-agent reinforcement learning, where the environment transition model is unknown and can only be learned via expensive interactions with the environment. We propose H-MARL (Hallucinated Multi-Agent Reinforcement…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…
This paper extends the framework of partially observable Markov decision processes (POMDPs) to multi-agent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the…