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We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
For a graph $G$, let $\Pi(G)$ denote the set of all potential maximal cliques of $G$. For each subset $\Pi$ of $\Pi(G)$, let $\tw(G, \Pi)$ denote the smallest $k$ such that there is a tree-decomposition of $G$ of width $k$ whose bags all…
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
This paper mainly investigates reflected stochastic recursive control problems governed by jump-diffusion dynamics. The system's state evolution is described by a stochastic differential equation driven by both Brownian motion and Poisson…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
Hamilton-Jacobi reachability (HJR) provides a value function that encodes the set of states from which a system with bounded control inputs can reach or avoid a target despite any bounded disturbance, and the corresponding robust, optimal…
We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
We investigate an application in the automatic tuning of computer codes, an area of research that has come to prominence alongside the recent rise of distributed scientific processing and heterogeneity in high-performance computing…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…
We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…
We consider a convexity constrained Hamilton-Jacobi-Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the…
In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law…
In this paper, we introduce GrAVITree, a tree- and sampling-based algorithm to compute a near-optimal value function and corresponding feedback policy for indefinite time-horizon, terminal state-constrained nonlinear optimal control…
Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input…
Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer…