Cheng, Lan
(2006)
Analysis and numerical solution of an inverse first passage problem from risk management.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We study the following "inverse first passage time" problem. Given a diffusion process Xt and aprobability distribution q(t) on t &ge 0, does there exist a boundary b(t) such that q(t)=P[&tau &ge t], where &tau is the first hitting time of Xt to the time dependent level b(t). We formulate the inverse first passage time probleminto a free boundary problem for a parabolic partial differential operator and prove there exists a unique viscosity solution to the associated Partial Differential Equation by using the classical penalization technique. In order to compute the free boundary with a given default probability distribution, we investigate the small time behavior of the boundary b(t), presenting both upper and lower bounds first. Then we derive some integral equations characterizing the boundary. Finally we apply Newtoniteration on one of them to compute the boundary. Also we compare our numerical scheme with some other existing ones.
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Details
Item Type: 
University of Pittsburgh ETD

Status: 
Unpublished 
Creators/Authors: 

ETD Committee: 

Date: 
7 July 2006 
Date Type: 
Completion 
Defense Date: 
20 October 2005 
Approval Date: 
7 July 2006 
Submission Date: 
30 November 2005 
Access Restriction: 
No restriction; Release the ETD for access worldwide immediately. 
Institution: 
University of Pittsburgh 
Schools and Programs: 
Dietrich School of Arts and Sciences > Mathematics 
Degree: 
PhD  Doctor of Philosophy 
Thesis Type: 
Doctoral Dissertation 
Refereed: 
Yes 
Uncontrolled Keywords: 
free boundary; upper bounds; viscosity 
Other ID: 
http://etd.library.pitt.edu/ETD/available/etd11302005121639/, etd11302005121639 
Date Deposited: 
10 Nov 2011 20:06 
Last Modified: 
15 Nov 2016 13:52 
URI: 
http://dscholarship.pitt.edu/id/eprint/9871 
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