Estimation in Financial Models - RiskLab

An Application
As an application of the above theory, we consider the linear stochastic differential
equation (3.27). The functions A, a, and B are assumed to be continuous
and given up to the unknown parameter 2 IR p . Under these
assumptions the stochastic dierential equation (3.27) has for every xed
x 0 2 IR d and 2 a unique solution given by
X t = t
x 0 +
Z t
0
,1
u a u du +
where is the deterministic d d matrix process solving
If
for all t>0 then
Z t
0
,1
u B u dW u ; t 0 ; (3.36)
d t = A t t dt; 0 = I d ; t 0: (3.37)
A t
Z t
0
Z t
A s ds = A s ds A t
0
Z t
t = exp
0
A s ds
is the unique solution to (3.37). We want to estimate from possibly incomplete
discrete observations of X at time-points 0 = t 0