RISK INS / 1.1 & 1.2
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48 Terms
Why Purely Discrete and Purely Continuous r.v.s are inadequate for modelling risks
CDF definition
CDF
discrete / continuous / mixed
converting to pdf
F(z) - F(z - 0) =
Why use Mixed Distributions?
How to set up Mixed Distribution
Degenerate Distributions in Insurance
Calculating Moments of Z
Mixed Distributions vs Mixture of r.v.s
A mixture of distributions (choosing between two worlds) is mathematically different from a mixture of random variables (adding two variables together).
The way they spread (variance) will be different.
E(X)
Cantor Distribution
Continuity vs Absolute Continuity
Using MGFs
MGF, PGF, CGF
Reinsurance
Stop-loss (re)insurance
Theorem
Net stop-loss premium
Theorem
Stop-loss transform
Theorem
Stop-loss is the most efficient form of reinsurance
Example:
when Proportional Reinsurance becomes the "optimal" choice instead of Stop-Loss:
Ordinary Deductible
= stop-loss for civilian instead of insurance company
Franchise Deductible
Expected Loss of Deductible
Ordinary and Franchise
First & Second Moment
Ordinary Deductible
Loss Elimination Ratio
Convolutions
in individual risk model
Convolutions
Formulating CDF, PMF, PDF
Convolutions
Properties + Examples
Calculating the distribution of the total claim amount
Setup + Notation
Calculating the distribution of the total claim amount
Distributions for N
E(S)
V(S)
mS(t)
Convolution formula for a compound CDF
Distribution of N
Poisson
Distribution of N
Negative Binomial
Relation
Poisson & Negative Binomial
Theorem
Sum of compound Poisson r.v.’s is compound Poisson
Theorem
Frequencies of claim sizes are …
3.22?
Definition
Poisson Process
Definition + E() + V()
Poisson Process
The Sparse Vector Algorithm
Individual and Collective Risk Model
Setup + Setting λ
Individual and Collective Risk Model
Comparison of Variance
Computational Advantages
Partial Fractions Decomposition
Stable Distributions
n-fold convolution
Negative Binomial vs Binomial
Negative Binomial vs Poisson
Compound Poisson Distribution
