Related papers: Piecewise Constant Policy Approximations to Hamilt…
In this paper, an optimization problem for the monotone mean-variance(MMV) criterion is considered in the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance(MV) criterion which…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale…
In this paper we consider a pairs trading financial market with the spread of risky assets defined by the Ornstein-Uhlenbeck (OU) process. We implement an optimal strategy for power utility functions for investment/consumption problem.…
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…
We prove comparison principle for viscosity solutions of a Hamilton-Jacobi-Bellman equation in a strong coupling regime considering a stationary and a time-dependent version of the equation. We consider a Hamiltonian that has a…
Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…
We introduce a Monte Carlo scheme for fully nonlinear parabolic nonlocal PDE's whose nonlinearity in of Hamilton-Jacobi-Bellman-Isaacs (HJBI for short). We avoid the difficulties of infinite L\'evy measure by truncation of the L\'evy…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
Here, we study the periodic homogenization problem of nonlinear weakly coupled systems of Hamilton-Jacobi equations in the convex setting. We establish a rate of convergence $O(\sqrt{\varepsilon})$ which is sharp.
In this paper, we analyse Lipschitz continuous dependence of the solution to Hamilton-Jacobi-Bellman equations on a functional parameter. This sensitivity analysis not only has the interest on its own, but also is important for the mean…
The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…
In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton--Jacobi--Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic…
We present a new efficient computational approach for time-dependent first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a time-implicit Eulerian discretization, the numerical scheme is unconditionally stable, but…
Solving the Hamilton-Jacobi-Bellman equation is important in many domains including control, robotics and economics. Especially for continuous control, solving this differential equation and its extension the Hamilton-Jacobi-Isaacs…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
Following the recent resurgence in establishing linear control theoretic benchmarks for reinforcement leaning (RL)-based policy optimization (PO) for complex dynamical systems with continuous state and action spaces, an optimal control…
We investigate high-order finite difference schemes for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Nondominated sorting is an algorithm for sorting points in Euclidean space into layers by repeatedly removing…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…