Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/boundary-sensitivities-for-diffusion-processes-in-time-dependent-aVgpuHRYtg
References (28)
-
E. Gobet, S. Menozzi (2004)
Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler schemeStochastic Processes and their Applications, 112
-
K. Brekke, B. Øksendal (1990)
The High Contact Principle as a Sufficiency Condition for Optimal Stopping -
Cristina Costantinia, Nicole Karouib, Emmanuel Gobetb (2003)
Représentation de Feynman–Kac dans des domaines temps–espace et sensibilité par rapport au domaineComptes Rendus Mathematique, 337
-
G. Lieberman (1996)
SECOND ORDER PARABOLIC DIFFERENTIAL EQUATIONS -
W. Fleming, H. Soner, H. Soner, Div Mathematics, Florence Fleming, Serpil Soner (1992)
Controlled Markov processes and viscosity solutions -
N. Karoui (1981)
Les Aspects Probabilistes Du Controle Stochastique -
(1964)
Functional integration and partial dierential equations, 1st edn Partial dierential equations of parabolic type -
M. Fu, S. Laprise, D. Madan, Yi-Hsun Su, Rongwen Wu (2001)
Pricing American Options: A Comparison of Monte Carlo Simulation Approaches ⁄Journal of Computational Finance, 4
-
C. Costantini (1992)
The Skorohod oblique reflection problem in domains with corners and application to stochastic differential equationsProbability Theory and Related Fields, 91
-
I. Karatzas (1988)
On the pricing of American optionsApplied Mathematics and Optimization, 17
-
E. Csáki, A. Földes, P. Salminen (1987)
On the joint distribution of the maximum and its location for a linear diffusionAnnales De L Institut Henri Poincare-probabilites Et Statistiques, 23
-
J. Sokołowski, J. Zolésio (1992)
Introduction to shape optimization -
A. Friedman (1983)
Partial Differential Equations of Parabolic Type -
T. Kurtz, P. Protter (1991)
Weak Limit Theorems for Stochastic Integrals and Stochastic Differential EquationsAnnals of Probability, 19
-
E. Gobet (2001)
Euler schemes and half-space approximation for the simulation of diffusion in a domainEsaim: Probability and Statistics, 5
-
Y. Saisho (1987)
Stochastic differential equations for multi-dimensional domain with reflecting boundaryProbability Theory and Related Fields, 74
-
S. Menozzi (2006)
Improved Simulation for the Killed Brownian Motion in a ConeSIAM J. Numer. Anal., 44
-
J. Simon (1980)
Differentiation with Respect to the Domain in Boundary Value ProblemsNumerical Functional Analysis and Optimization, 2
-
P. Cattiaux (1991)
Calcul stochastique et opérateurs dégénérés du second ordre. II: Problème de DirichletBulletin Des Sciences Mathematiques, 115
-
BY Aronson, J. Oser (1967)
Bounds for the fundamental solution of a parabolic equationBulletin of the American Mathematical Society, 73
-
M. James (1994)
Controlled markov processes and viscosity solutionsStochastics and Stochastics Reports, 49
-
H. Soner, S. Shreve (1991)
A free boundary problem related to singular stochastic control: the parabolic caseCommunications in Partial Differential Equations, 16
-
(1985)
Functional integration and partial di erential equations, 1st edn -
G. Lieberman (1986)
Intermediate Schauder theory for second order parabolic equations II -
R. Durrett (1984)
Brownian motion and martingales in analysis -
(2002)
Shape optimization by the homogeneization method, 1st edn -
S. Shreve (1988)
An Introduction to Singular Stochastic Control, 10
-
F. Murat, J. Simon (1975)
Etude de Problème d'Optimal Design
- Publisher
- Springer Journals
- Copyright
- Copyright © 2006 by Springer
- Subject
- Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-006-0863-4
- Publisher site
- See Article on Publisher Site
Abstract
We study the sensitivity, with respect to a time dependent domain ${\cal D}_s,$ of expectations of functionals of a diffusion process stopped at the exit from ${\cal D}_s$ or normally reflected at the boundary of ${\cal D}_s.$ We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pricing of American options, to singular stochastic control and others are discussed.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Sep 1, 2006