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Analysis and numerical solution of an inverse first passage problem from risk management

Cheng, Lan (2006) Analysis and numerical solution of an inverse first passage problem from risk management. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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 Newton-iteration 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Status: Unpublished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:
CreatorsEmailPitt UsernameORCID
Cheng, LanLan.Cheng@fredonia.edu
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChen, Xinfuxinfu@pitt.eduXINFU
Committee CoChairChadam, Johnchadam@pitt.eduCHADAM
Committee MemberSaunders, Daviddsaunder@math.uwaterloo.ca
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Committee MemberNamoro, Soiliou Dawsnamoro@pitt.eduSNAMORO
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/etd-11302005-121639/, etd-11302005-121639
Date Deposited: 10 Nov 2011 20:06
Last Modified: 15 Nov 2016 13:52
URI: http://d-scholarship.pitt.edu/id/eprint/9871

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