A Filtering Model on Default Risk

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 1, Page 107--142.

Nakagawa, Hidetoshi
A Filtering Model on Default Risk
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Abstract:
In this paper, we present a filtering model on a default risk related to mathematical finance. We regard as the time when a default occurs the first hitting time at zero of a one dimensional process which starts at some positive number and is not directly observed. We discuss the conditional law of the hitting time under imperfect information. We use the reference measure change technique and a new formula on a kind of conditional expectation to obtain a so-called hazard rate process. It is also discussed what the relation between the hazard rate process and the conditional law of the hitting time is like.

Mathematics Subject Classification (1991): Primary 60G35; Secondary 60H05, 60H30
Mathematical Reviews Number: MR1818908

Received: 2000-07-03