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In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
We analyze the problem of optimal reduction of the debt-to-GDP ratio in a stochastic control setting. The debt-to-GDP dynamics are modeled through a stochastic differential equation in which fiscal policy simultaneously affects both debt…
The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
Option contracts on two underlying assets within uncertain volatility models have their worst-case and best-case prices determined by a two-dimensional (2D) Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with…
We tackle the problem of bias mitigation of algorithmic decisions in a setting where both the output of the algorithm and the sensitive variable are continuous. Most of prior work deals with discrete sensitive variables, meaning that the…
We consider a long-run impulse control problem for a generic Markov process with a multiplicative reward functional. We construct a solution to the associated Bellman equation and provide a verification result. The argument is based on the…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…
It is well known that the extension of Watkins' algorithm to general function approximation settings is challenging: does the projected Bellman equation have a solution? If so, is the solution useful in the sense of generating a good…
We investigate the application of Weak Poincar\'e Inequalities (WPI) to Markov chains to study their rates of convergence and to derive complexity bounds. At a theoretical level we investigate the necessity of the existence of WPIs to…
When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the…
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…
Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
We provide a data-driven framework for optimal control of a continuous-time stochastic dynamical system. The proposed framework relies on the linear operator theory involving linear Perron-Frobenius (P-F) and Koopman operators. Our first…