Related papers: A free boundary problem arising from a multi-state…
We study a free transmission problem driven by degenerate fully nonlinear operators. Our first result concerns the existence of solutions to the associated Dirichlet problem. By framing the equation in the context of viscosity inequalities,…
We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be…
In this paper, we examine a modified version of de Finetti's optimal dividend problem, incorporating fixed transaction costs and altering the surplus process by introducing two-valued drift and two-valued volatility coefficients. This…
We consider the problem of the optimal trading strategy in the presence of a price predictor, linear trading costs and a quadratic risk control. The solution is known to be a band system, a policy that induces a no-trading zone in the…
This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper…
This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary.…
We investigate singular and degenerate behavior of solutions of the unstable free boundary problem $$\Delta u = -\chi_{\{u>0\}} .$$ First, we construct a solution that is not of class $C^{1,1}$ and whose free boundary consists of four arcs…
In this paper we propose a mathematical framework to address the uncertainty emergingwhen the designer of a trading algorithm uses a threshold on a signal as a control. We rely ona theorem by Benveniste and Priouret to deduce our Inventory…
This paper is concerned with the study of the behavior of the free boundary for a class of solutions to a one-phase Bernoulli free boundary problem with mixed periodic-Dirichlet boundary conditions. It is shown that if the free boundary of…
In this paper we present a survey concerning unconstrained free boundary problems of type $$ \left\{ \begin{array}{ll} F_1(D^2u,\nabla u,u,x)=0 & \text{in }B_1 \cap \Omega ,\\ F_2 (D^2 u,\nabla u,u,x)=0 & \text{in }B_1\setminus\Omega ,\\ u…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied…
This paper concerns the theoretical and numerical analysis of a free boundary problem for the Laplace equation, with a curvature condition on the free boundary. This boundary is described as the graph of a function, and contact angles are…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We study a variant of the Alt, Caffarelli, and Friedman free boundary problem with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schr\"odinger operator in a…
We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of…
We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly…
Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…
This paper studies a sequential decision problem where payoff distributions are known and where the riskiness of payoffs matters. Equivalently, it studies sequential choice from a repeated set of independent lotteries. The decision-maker is…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…