I
Brownian motion aka Wiener Process: SDE

cfw_I . I cfw_ cfw_ cfw_ . Jcfw_ $ cfw_ . Jcfw_ H cfw_ cfw_
I"
I cfw_
Increments are independent and indept of I i.e Jcfw_I , I . I cfw_
$ cfw_
Standard B.M:
"
Jcfw_ cfw_
and
(i.e Set
H cfw_ cfw_
cfw_J cf
Stochastic Processes: Let , , be a probability space with , drift coefficient, , diffusion coefficient
information structure given by = , 0,
Geometric Brownian Motion: = + OR
= exp = +
Information structure defined by a sequence of partitions:
At time
NCD Systems
To adjust the transition matrix: Pr(Claim) = Pr(Claim  Loss) Pr(Loss).
Expected Claims = Pr(Claim) (Avg. claim size  Loss > x) where x is the
minimum loss size needed to make a claim (calculate from table).
NCD category at time 0
Year 1
Prem
George Liu 41788974  2011
Sigma algebra and filtration = : . . ,2,1,0 =
a collection of subsets of , is a sigmaalgebra on if:
1. , 2. , 3.
Contidional Expectation: () =  1
Consider all  where event
= + = =
sub
is a
martingale if ( ) < a