# Boundary Sensitivities for Diffusion Processes in Time Dependent Domains

Boundary Sensitivities for Diffusion Processes in Time Dependent Domains 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Boundary Sensitivities for Diffusion Processes in Time Dependent Domains

, Volume 54 (2) – Sep 1, 2006
29 pages

/lp/springer_journal/boundary-sensitivities-for-diffusion-processes-in-time-dependent-aVgpuHRYtg
Publisher
Springer-Verlag
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
D.O.I.
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 OptimizationSpringer Journals

Published: Sep 1, 2006

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations