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On the Principle of Smooth Fit for Killed Diffusions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On the Principle of Smooth Fit for Killed Diffusions
2.	Creator	Author's name, affiliation, country	Farman Samee; University of Manchester
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Optimal stopping; discounted optimal stopping; principle of smooth fit; regular diffusion process; killed diffusion process; scale function; concave function
3.	Subject	Subject classification	Primary 60G40; Secondary 60J60
4.	Description	Abstract	We explore the principle of smooth fit in the case of the discounted optimal stopping problem $$ V(x)=\sup_\tau\, \mathsf{E}_x[e^{-\beta\tau}G(X_\tau)]. $$ We show that there exists a regular diffusion $X$ and differentiable gain function $G$ such that the value function $V$ above fails to satisfy the smooth fit condition $V'(b)=G'(b)$ at the optimal stopping point $b$. However, if the fundamental solutions $\psi$ and $\phi$ of the `killed' generator equation $L_X u(x) - \beta u(x) =0$ are differentiable at $b$ then the smooth fit condition $V'(b)=G'(b)$ holds (whenever $X$ is regular and $G$ is differentiable at $b$). We give an example showing that this can happen even when `smooth fit through scale' (in the sense of the discounted problem) fails.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-03-22
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1531
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1531
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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