Related papers: Smooth Value Functions for a Class of Nonsmooth Ut…
In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or…
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections…
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…
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…
We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the…
In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle this problem we chose a continuous forward-backward approach and…
This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has a nonsmooth coefficient and the dual method developed in [6] does not work. We…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated…
This note lays part of the theoretical ground for a definition of differential systems modeling reinforcement learning in continuous time non-Markovian rough environments. Specifically we focus on optimal relaxed control of rough equations…
Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…
In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear…
We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This HJB equation is related to a stochastic optimal control problem for which…
We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this…
This paper studies an optimal consumption-investment problem for an investor whose instantaneous utility depends on both consumption and wealth, and the investor faces a general borrowing constraint that the investment amount in the risky…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…