The Universal Principle of Risk Management: Pooling and the
Hedging of Risks
LINK
SUMMARY
It is interesting that the concept of probability and statistic were appeared relatively late in the history, after 17 century. Today's class reviewed all principals in mathematics aspect. 1) Independent theory 2) Multiplication theory 3) Sampling/Geometric average 4) variance/co-variance 5) Gaussian distribution 6) PV
NOTES
It is interesting that the concept of probability and statistic were appeared relatively late in the history, after 17 century. Today's class reviewed all principals in mathematics aspect. 1) Independent theory 2) Multiplication theory 3) Sampling/Geometric average 4) variance/co-variance 5) Gaussian distribution 6) PV
NOTES
1. Historical introduction
Probability
1600 <
17 century
Probable … trust
worthy ness , in Shakespeare
Probability theory / sampling theory - Nala M.
Life table – insurance – ancient Rome
In Renaissance Italy – insurance policy started
Slow start of insurance in history – due to no lack of probability concept, no
clear meaning
Luck / Risk – the theory is away
from this.
2. Principals
P: Prob 0<= P
<= 1 (basic)
·
Independent
Theory
Independence (Independent
Event)
·
Multiplication
rule
P(A & B) = P(A) * P(B)
i.e. Fire in London
No risk of whole city burn down for insurance company
·
Binominal
Distributor
F(x) = P^x (1-P) ^(n-x) n!/(n-x) !
# of accidents
·
Expected
Value, Mean, Average
x : Random Variable
Population E(x) = Myu
x = (Sum i= 1-infinit) P(x-xi)xi
Average Sum(i=1-n) xi/n
·
Sampling
Ave.
·
G(x) =
Geometric average : multiply all and ^1/n -- Finance use to expect returns
- lower number then E(x)
Experiment
E(x) = Myu x = Integral –infinit to + infinit f(x)x dx
Variance Sigma S^2 Standard Deviation
·
Population
Variance Var(x) = Sum P(x-xi_(xi-u)^2
S(x)^2 = Sum (x-xbar)^2/n – Sample variance
·
Covariance
(2 random variables)
C(x,y) = Sum (xi -xbar)(yi -ybar)/n
Negative / positive
Move differently / move together
Correlation
Corr -1 ~ <= P <= +1
P=Cov(x,y)/SxSy
·
Regression – Gauss
Y=Return on A Inc.
X= Return on MKT
Regression line
Alpha (Y(X0)) &
Beta (slope)
A’s Performance in
the market
·
Normal
Distribution – Gaussian distribution
Bell Shape Curve
Fat Tailed distribution
= lots of returns
(+) Right tail / (-) Left tail
·
Present
Values PV
·
Console
or Perpetuity
- Annuity
- Utility function
