Analysis of an Inverse First Passage Problem from Risk Management | Zendy

Lan Cheng | Zendy; Xinfu Chen | Zendy; John Chadam | Zendy; David Saunders | Zendy

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Analysis of an Inverse First Passage Problem from Risk Management

Author(s) -

Lan Cheng,

Xinfu Chen,

John Chadam,

David Saunders

Publication year - 2006

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/050622651

Subject(s) - mathematics , uniqueness , boundary (topology) , inverse , inverse problem , mathematical analysis , operator (biology) , boundary value problem , first hitting time model , distribution (mathematics) , upper and lower bounds , diffusion , combinatorics , geometry , physics , biochemistry , chemistry , statistics , repressor , transcription factor , gene , thermodynamics

We study the following "inverse first passage time" problem. Given a diusion process Xt and a probability distribution q on (0,1), does there exist a boundary b(t) such that q(t) = P( t), where is the first hitting time of Xt to the time dependent level b(t). A free boundary problem for a parabolic partial dierential operator is associated with the inverse first passage time problem. We prove the existence and uniqueness of a viscosity solution to this equation. We also investigate the small time behavior of the boundary b(t), presenting both upper and lower bounds. Finally, we derive some integral equations charaterizing the boundary.

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