On a PDE Arising in One-Dimensional Stochastic Control Problems
نویسندگان
چکیده
The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one–dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous–time portfolio problems.
منابع مشابه
A Note on the Continuity of Free-Boundaries in Finite-Horizon Optimal Stopping Problems for One-Dimensional Diffusions
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one-dimensional, time-homogeneous stochastic differential equation (SDE). The proof relies on both analytic and probabilistic arguments and it is based on a contradict...
متن کاملCovariance Control Problems over Martingales with Fixed Terminal Distribution Arising from Game Theory
We study several aspects of covariance control problems over martingale processes in Rd with constraints on the terminal distribution, arising from the theory of repeated games with incomplete information. We show that these control problems are the limits of discrete-time stochastic optimization problems called problems of maximal variation of martingales meaning that sequences of optimizers f...
متن کاملContinuous Dependence Estimates for Viscosity Solutions of Integro-pdes
We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. M...
متن کاملNew variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملAn Iterative Path Integral Stochastic Optimal Control Approach for Learning Robotic Tasks
Recent work on path integral stochastic optimal control theory Theodorou et al. (2010a); Theodorou (2011) has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Optimization Theory and Applications
دوره 147 شماره
صفحات -
تاریخ انتشار 2010