April 2011
Intermediate to advanced
328 pages
9h 5m
English
Content preview from Risk Analysis in Finance and Insurance, 2nd Edition
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180 Risk Analysis in Finance and Insurance
Since evolution of prices in the problem of quickest detection of tenden-
cies is described in terms of stochastic processes, one can consider a slightly
different setting of that problem. Namely, one solves a problem of quickest
detection of time when the probabilistic characteristics of the stochastic pro-
cess change. This problem is referred to as a change point problem, and it was
introduced by Kolmogorov and Shiryaev.
It is convenient to specify process X in the following way:
dX
t
=
σdW
t
, if t<θ
rdt+ σdW
t
, if t ≥ θ
.
The stopping time τ adapted to observations of process X can be inter-
preted as an alarm t ...
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