Related papers: On the One-Dimensional Optimal Switching Problem
We revisit the inverted pendulum problem with the goal of understanding and computing the true optimal value function. We start with an observation that the true optimal value function must be nonsmooth ($i.e.$, not globally $C^1$) due to…
By using the Onsager variational principle as an approximation tool, we develop a new diffusion generated motion method for wetting problems. The method uses a signed distance function to represent the interface between the liquid and vapor…
We mainly study numerical integration of real valued functions defined on the $d$-dimensional unit cube with all partial derivatives up to some finite order $r\ge1$ bounded by one. It is well known that optimal algorithms that use $n$…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
This paper investigates the robustness of stochastic optimal control for controlled regime switching diffusions. We consider systems driven by both continuous fluctuations and discrete regime changes, allowing for model misspecification in…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
In this paper, we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…
We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability…
Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
A finite horizon optimal stopping problem for an infinite dimensional diffusion $X$ is analyzed by means of variational techniques. The diffusion is driven by a SDE on a Hilbert space $\mathcal{H}$ with a non-linear diffusion coefficient…
In this paper we formulate and study an optimal switching problem under partial information. In our model the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by $g$-evaluations. For such problems, we…