A study of the free boundary of a two-dimensional singular stochastic control problem
نویسنده
چکیده
A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the free boundary between the control and no-action regions is approximately linear away from the state constraining boundaries. Proof of this result relies on connections with related optimal stopping problems. We provide an explicit solution to one such optimal stopping problem. Results of a numerical study of the free boundary and optimal value function are presented.
منابع مشابه
A two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملNumerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...
متن کاملA study of the free boundary of a two-dimensional singular
A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the free boundary between the control and no-action regions is approximately linear away from the state constraining boundaries. Proof of this result relies on connections with related optimal stopping problems. We provide an explicit solution to one such optimal stopping problem. Results of ...
متن کاملNonlinear Two-Phase Stefan Problem
In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.
متن کاملA boundary element study for evaluation of the effects of the rigid baffles on liquid sloshing in rigid containers
In this paper, the sloshing response of liquid in a two dimensional rigid rectangular tank with rigid baffles is investigated using boundary element technique. A baffle is a supplementary structural element which supplies a kind of passive control on the effects of ground shaking. The complicated liquid domain is divided into two simple sub-domains so that the liquid velocity potential in each ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008