1. Real-time risk analysis – elements of Large Deviation Theory http://www.hit.bme.hu/~ceffer/pir

2. Motivation with a pre-defined system risk Financial Institutions
High utilization
with a pre-defined system risk
Account holders
Elementary statistical descriptors
Financial Institution R M A y n
Maintained risk policy
Objective: Real Time risk analysis methods which maintain a pre-defined risk policy but maximize system utilization !

3. The model
Component description

4. The model (cont.)
System description

5. Calculation of system risk:
The model (cont.)
Calculation of system risk:
This is not real time, what to do?

6. The program
i:=1, a:=0
y:=binconv(i)
i:=i+1 y
a:=a +
RESULT n
END

7. Large deviation theory – Statistical inequalities
Markov inequality p
yes OK h C

8. The Chernoff bound Log moment gen. function
The log moment gen. function is additive :

9. The log moment generating functions

10. Satisfying the system risk criterion
Statistical (risk) “bandwidth”
Available overall “bandwidth” under given risk level

11. The program
Start
Input: p,h,
C:=C+E No
Yes
End