Brownian motion aka Wiener Process: SDE
cfw_I . I cfw_ cfw_ cfw_ . Jcfw_ $ cfw_ . Jcfw_ H cfw_ cfw_
Increments are independent and indept of I i.e Jcfw_I , I . I cfw_
H cfw_ cfw_
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:
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
George Liu 41788974 - 2011
Sigma algebra and filtration = : . . ,2,1,0 =
a collection of subsets of , is a sigma-algebra on if:
1. , 2. , 3.
Contidional Expectation: (|) = | 1
Consider all | where event
= + = =
-martingale if |( |) < a