Related papers: A free boundary problem arising from a multi-state…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
We consider a PDE-constrained optimization problem governed by a free boundary problem. The state system is based on coupling the Laplace equation in the bulk with a Young-Laplace equation on the free boundary to account for surface…
In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation,…
A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of…
We introduce a new geometric-analytic functional that we analyse in the context of free discontinuity problems. Its main feature is that the geometric term (the length of the jump set) appears with negative sign. This is motivated by…
Given the marginal distribution information of the underlying asset price at two future times $T_1$ and $T_2$, we consider the problem of determining a model-free upper bound on the price of a class of American options that must be…
This paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a…
We consider the free boundary problem for the incompressible elastodynamics equations. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure…
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…
We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear…
In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics.…
In this paper we study the two-phase Bernoulli type free boundary problem arising from the minimization of the functional $$ J(u):=\int_{\Omega}|\nabla u|^p +\lambda_+^p\,\chi_{\{u>0\}} +\lambda_-^p\,\chi_{\{u\le 0\}}, \quad 1<p<\infty. $$…
In this paper, we study a free boundary problem for a class of nonlinear nonautonomous size structured population model. Using the comparison principle and upper lower solution methods, we establish the existence of the solution for such…
In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price…
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…
We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…