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Statistical Methods with Applications to Demography and Life Insurance
book

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
March 2013
Intermediate to advanced content levelIntermediate to advanced
242 pages
5h 47m
English
Chapman and Hall/CRC
Content preview from Statistical Methods with Applications to Demography and Life Insurance
202 Population dynamics
is again a martingale. If one were to think about hMi(t) as a sum of
conditional variances, the process hM
1
,M
2
i(t) could be thought of as
the sum of the conditional covariances E[dM
1
(t)dM
2
(t)|F
t
]. Martin-
gales M
1
(t) and M
2
(t) are called orthogonal if hM
1
,M
2
i(t) = 0 for all
t. From the condition (16.8) on their jump points, then, we have shown
that the martingales M
B
and M
D
are orthogonal.
Now let us return to the equality (16.5). Being a definition of M,
this equality is simply an identity. However, let us assume that M is
given and consider (16.5) as an equation with respect to P: the solution
of
dP(t) = cP(t)dt + dM(t)
is given by
P(t) =
Z
t
0
e
c(ts)
dM(s) + e
ct
P(0). (16.10)
This representation describes properties of the population ...
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Publisher Resources

ISBN: 9781466505742